Remember that vertical lines only have a 'y' value and no 'x' value. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. To find the equation of a line when given two points on the line, we first find the slope and then find the y-intercept. To graph a horizontal line that goes through a given point, first plot that point. Substituting the value of k in equation (i), we get. 4 years ago. So we'll go with undefined. x = a, where a is the x-intercept. To graph a vertical line that goes through a given point, first plot that point. Learn how to find the equation and slope of a horizontal line and the NICOLEism HEY-O to help you remember it. Determine if the line shown in Fig 1 is vertical and write its equation. The equation of a vertical line in the graph, which is parallel to y-axis is x = a. Both of our points have an x-coordinate of $$−2$$. Vertical Lines . and we have a vertical line , say for example, x = 31; we might try algrebraically == y=mx + b >> y-b = mx >> x = (y - b )/m . Horizontal & vertical lines. Therefore the equation for a vertical line passing through this point is: x = 8 Likewise, for a horizontal line the value of y, in this case color(red)(-7), will never change. Viewed 84k times 20. Graph the vertical line x = 3.. In an example equation a vertical line is given the expression x = k. Then draw a straight line up and down that goes through the point, and you're done! Vertical line. The Corbettmaths Practice Questions on the Equation of a Line. Site Navigation. Let's do one more. ( link) For instance in the graph below, the vertical line has the equation x = 2 As you can see in the picture below, the line goes straight up and down at … A vertical line has a slope that is undefined. Thus the equation of the vertical line through (6, … If you're seeing this message, it means we're having trouble loading external resources on our website. You may be able to guess that vertical lines are lines that go straight up and down, but did you know that all vertical lines have the same slope? Active 10 months ago. How to write the equation of vertical and horizontal lines? Example 3: The equation of a vertical line that passes through the point (-2 , -5) may be written as follows: x = - 2 4 - Equation of a Horizontal Line y = k, where k is a constant. This is precisely the interpretation of the equation x = 3. line m = 4, ( −1, − 6) $line\:\left (-2,\:4\right),\:\left (1,\:2\right)$. When the slope is undefined then the line is vertical. Free line equation calculator - find the equation of a line step-by-step. vertical line is not defined, since the run is 0. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! The differential equation of all vertical lines in a plane is? In coordinate geometry, a vertical line is parallel to the y-axis on the coordinate plane. Since vertical line equations are simply the x-intercepts, we know that the "3" gives us all the info we'll need to solve this problem. Ask Question Asked 10 years ago. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! The first coordinate in each pair is the x-coordinate which are -15, and -15. The first half of this page will focus on writing the equation in slope intercept form like example 1 below.. That is, every x -value of a function must be paired to a single y -value . Equation of a vertical line The equation of a line has several forms, but let's take the slope intercept form for this explanation. The second part requires you to draw horizontal and vertical lines given the equation. To graph a horizontal line that goes through a given point, first plot that point. Since they are equal, the line is vertical. Follow along with this tutorial as you see how use the information given to write the equation of a vertical line. There are various ways of defining a line. We often think of a vertical line as being the opposite of a horizontal line.. In the following subsections, a linear equation of the line is given in each case. The second line's equation was y = –2 x + 3, and the line's slope was m = –2.. Take special note what undefined means here, the slope of a vertical line not defined because it is a line pointing straight up, making it approach infinity as a value in the limit. The x-coordinate of every point on the graph is 6. To check whether the relation is a function in maths, we use a vertical line. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero. Horizontal and Vertical Lines. In an example equation a vertical line is given the expression x = k. Next, you may be interested in learning how to conduct a vertical line test. Examples. Since the given vertical line passes through the point (-4, 7) so from equation (i), we have. Click a subject below to view more math questions: Either part can be omitted. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! To see this process in action, watch this tutorial! Like all vertical lines, it has to have an equation of the form x = K. So let’s think about this, we’re gonna look at the triangle and give the vertices letter names. Want to take a look at different equations for vertical lines? It is a vertical line. How Do You Write an Equation for a Horizontal Line? In coordinate geometry, a vertical line is parallel to the y-axis on the coordinate plane. Practice your knowledge of horizontal and vertical lines: their graphical presentation, their slopes, and their equations. Horizontal & vertical lines. NO! By using this website, you agree to our Cookie Policy. Since there is no y, we cannot write it in slope-intercept form. Show Step-by-step Solutions. Thus, the equation is y = 2. Trying to find the equation of a horizontal line that goes through a given point? So our equation of the line is $$x=−2$$. Its equation is x is equal to negative five. Remember that vertical lines only have an 'x' value and no 'y' value. Trying to find the equation of a horizontal line that goes through a given point? Equation = x=3. Trying to find the equation of a horizontal line that goes through a given point? Equation of a vertical line. Write an equation of a vertical line that crosses the x-axis (-1,0): Since line is vertical, y = x. How to Find the Vertical Tangent. Lv 4. Slope of a horizontal line. Furthermore if a point in the plane is not on the graph then its x-coordinate is not 6. The slope is undefined... and where does it cross the Y-Axis? Hope this was helpful. Example 3: The equation of a vertical line that passes through the point (-2 , -5) may be written as follows: x = - 2 4 - Equation of a Horizontal Line y = k, where k is a constant. Equation of the horizontal line will be in the form x = h So the equation of a vertical line will always be expressed as x = a (shared coordinate). This website uses cookies to ensure you get the best experience. Khan Academy is a 501(c)(3) nonprofit organization. If you consider what the slope looks like for a vertical line, it's an infinite slope. All the points on the vertical line below have an x-coordinate. Donate or volunteer today! Thus the equation of the vertical line through (6, -2) is x = 6. Hence a point (x,y) in the plane is on the graph if and only is x = 6. slope 3x + 3y − 6 = 0. Slope intercept vs Point Slope Form. Equation of a line. The points A and B on the line are at (-15,3) and (-15,20). Expect that there are two vertical lines (one to the left of the x-intercept, and one to the right) that will form the triangles stated in the above problem. Where #a# is some real number on the x axis.. Why not check out this online slider to see vertical lines that cross the x-intercept at different points. X doesn't change. he differential equation of all non-vertical lines in a plane is (A) d^2y/dx^2 = 0 (B) d^2x/dy^2 = 0 asked Jan 2, 2020 in Differential equations by Sarita01 ( 53.4k points) differential equations You may be able to guess that vertical lines are lines that go straight up and down, but did you know that all vertical lines have the same slope? Explanation: Vertical lines are lines that go straight up and down. Up Next. Equations of vertical lines: The very first equation which you should use which involves a vertical line is the formula ofvertical lines, which is fairly straight forward and easy to understand. Videos, worksheets, 5-a-day and much more Does your graph agree with our conclusion that this is a vertical line? You can measure the length of a vertical or horizontal line on a coordinate plane by simply counting coordinates; however, measuring the length of a diagonal line is trickier. Trying to find the equation of a vertical line that goes through a given point? All vertical line graphs have an equation of the form: $x = c$ If we're talking about a vertical line, that means that x doesn't change. The equation doesn’t have the variable y which implies that it could assume any numerical values for y.In the table of values, you will see that “ 3 ” is the repeating value in the column of x while having different values in the column of y. Instead of $\vline$ or $|$, does anyone know a way to draw this vertical line of desired length? The x is actually vertical and the y is actually horizontal. Thus, the equation for a vertical line is x = a, where a is the value that x takes. This will be true for any value of y. To see this process in action, watch this tutorial! When a slope is equal to zero, the line is horizontal. In the above graph, the line x = -1 is parallel to y axis, hence it is vertical line. Take special note what undefined means here, the slope of a vertical line not defined because it is a line pointing straight up, making it approach infinity as a value … The equation of a vertical line in the graph, which is parallel to y-axis is x = a. Learn more Accept. A non-vertical line can be defined by its slope m, and its y-intercept y 0 (the y coordinate of its intersection with the y-axis). 3 - Equation of a Vertical Line x = k, where k is a constant. Below is the graph of a vertical line that has an x-intercept of (h, 0). So, let me do this without even drawing it. The equation of a vertical line does not have a y-intercept since a vertical line never crosses the y-axis and the slope of a vertical line is undefined because the denominator of … I am writing a big formula where a vertical line is needed. x = a, Two lines are parallel if their slopes are equal. Then draw a straight line up and down that goes through the point, and you're done! How Do You Write an Equation for a Horizontal Line. For example, x=0 is the equation of a vertical line through the origin (0,0). What is the equation for a vertical line? Similarly, in the graph of a vertical line, x only takes one value. All points that lie on a vertical line have the same {eq}x{/eq}-coordinate. Equation of a Vertical Line: An equation that takes the form {eq}x=c{/eq} represents a vertical line. So, if we're talking about a vertical. The slope of a vertical line is infinity or undefined as it has no y-intercept and the denominator in the slope formula is zero. Vertical line. We often think of a vertical line as being the opposite of a horizontal line.. The first part requires you to write down the equation of horizontal and vertical lines. 3 - Equation of a Vertical Line x = k, where k is a constant. In this tutorial, learn all about vertical lines including their slope and what the equation of a vertical line looks like! General Steps to find the vertical tangent in calculus and the gradient of a curve: Types of problems Write down the equation Draw the line. The vertical line test supports the definition of a function. slopes of horizontal and vertical lines The slope of a line is the ratio of rise to run for any two points on the line. Thus, the required equation of the line is. About. Instead, the equation of a vertical line is in the form . Remember that vertical lines only have a 'y' value and no 'x' value. (2,4),(2,56) and (2,23.876) are all on your line, right? All points that lie on a vertical line have the same {eq}x{/eq}-coordinate. This tells us it is a vertical line. Explaining why a vertical line doesn't represent a function. add a comment + 5. vote up Answer by pradhaprajgmailcom (1518) Definition: A straight line on the coordinate plane where all points on the line have the same x-coordinate. If this line segment is on a dot grid, every line between two dots is one unit. Equations of vertical lines: The very first equation which you should use which involves a vertical line is the formula ofvertical lines, which is fairly straight forward and easy to understand. but then how do we make this fit x = 31. especially for the range of all y? For x=a there will be a VERTICAL line at the x-coordinate of "a" For y=b there will be a HORIZONTAL line at the y-coordinate of "b" Think of this as two opposites. The first coordinate in each pair is the x-coordinate which are -15, and -15. What that means is that you cannot have a y-value in your equation: x = 3. Trying to find the equation of a horizontal line that goes through a given point? On a graph, it runs parallel to the y-axis. 0 0. cerchia. A non-vertical line can be defined by its slope m, and its y-intercept y 0 (the y coordinate of its intersection with the y-axis). The equations of vertical and horizontal lines do not require any of the preceding formulas, although we can use the formulas to prove that the equations are correct. Horizontal and vertical lines are unique linear equations. The line leans to the right because the slope is positive. A tangent of a curve is a line that touches the curve at one point.It has the same slope as the curve at that point. The points A and B on the line are at (-15,3) and (-15,20). To see this process in action, watch this tutorial! Equation of a line. S.20 Equations of horizontal and vertical lines. The slope-intercept equation looks like the following: y = mx + b If we think of a vertical line as an infinite set of x -values , then intersecting the graph of a relation at exactly one point by a vertical line implies that a single x -value is only paired to a unique value of y . Therefore y = -1. A vertical line is going to have an undefined slope. The equation of every vertical line has the form where a is the x-intercept. Since the line crosses the x-axis at -15, the equation of the line is How Do You Write an Equation for a Horizontal Line. This will be true for any value of x. Vertical lines come in the form x = h. The vertical line x = h crosses with the given equation 2y - 3x = 6 at x = h and y = 1.5h + 3. The equation of a vertical line is: #x=a#. Remember that vertical lines only have a 'y' value and no 'x' value. Remember that vertical lines only have a 'y' value and no 'x' value. Slope–intercept form. a vertical line is always parallel to the y-axis and is of the form . Best regards! This relationship always holds true: If the line's equation is in the form "y=", then the number multiplied on x is the value of the slope m. Then draw a straight line left and right that goes through the point, and you're done! Follow along with this tutorial as you see how use the information given to write the equation of a vertical line. Find an equation of the vertical line that passes through … Trying to find the equation of a vertical line that goes through a given point? slope = rise / run = change in y / change in x If the line segment is on a coordinate plane, then you can do the same or use the distance formula for a line. Put your answer in fully reduced point-slope form and left it is a vertical or horizontal line I'll draw it right after that. There are various ways of defining a line. Instead, the equation of a vertical line is in the form x = a, where a is the x-intercept. Tutor. line ( −2, 4), ( 1, 2) $slope\:3x+3y-6=0$. Then, plug the slope into the slope-intercept formula, or y = mx + b, where "m" is the slope and "x" and "y" are one set of coordinates on the line. In the following subsections, a linear equation of the line is given in each case. Since they are equal, the line is vertical.Since the line crosses the x-axis at -15, the equation of the line is When a slope is equal to zero, the line is horizontal. The equation for line d is negative 2 y because that is where the line crosses the y axis a so it is y= negative 2 the vertical line (C) has an equation of x = negative 3 whenever you have a vertical line it is x equals and a horizontal line is y equals that constant. The line which is perpendicular to x-axis is known as vertical line. How to draw a vertical line of desired length in equations. x = -3. The equation of a vertical line always takes the form x = k, where k is any number and k is also the x-intercept . Save worksheet. Best regards! To find the equation of a line using 2 points, start by finding the slope of the line by plugging the 2 sets of coordinates into the formula for slope. To find the equation of a line when given two points on the line, we first find the slope and then find the y-intercept. How Do You Write an Equation for a Horizontal Line? You can use the Distance Formula to find the length of such a line. Report Paul M. answered • 06/06/19. A vertical tangent touches the curve at a point where the gradient (slope) of the curve is infinite and undefined. Slope–intercept form. K8H. Option (D) is CORRECT. Calculus Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach Find an equation of the vertical line that passes through (0, 5). 9. This would be a vertical line that passes through all y-values for x = 3. We will also learn how to determine the equation of a vertical line or a horizontal line given two points on the line. An equation of a line through a point P(x 1, y 1) with slope m is given by y - y 1 = m(x - x 1) Vertical and Horizontal lines: a - If we set A to zero in the general equation, we obtain an equation in y only of the form B y = C which gives y = C / B = k; k is a constant. Equation of a Vertical Line: An equation that takes the form {eq}x=c{/eq} represents a vertical line. Think about the graph of the vertical line through (6, -2). Write the equation of the line that passes through the points (-3,-7) and (-3,-4). If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. The equation of a vertical line does not have a y-intercept since a vertical line never crosses the y-axis and the slope of a vertical line is undefined because the denominator of the slope (the change in X) is zero. There are a few different ways to find the equation of line from 2 points.. Further Exploration. Draw a line between points A and B on the ground level.This is a vertical line… Therefore, it cannot be written in slope-intercept form. In both cases, the number multiplied on the variable x was also the value of the slope for that line. View solution The differential equation which represents the family of curves y = c 1 e c 2 x , where c 1 and c 2 are arbitrary constants, is The slope is the ratio of the change in the y-value over the change in the x-value. To check whether the relation is a function in maths, we use a vertical line. Lines In the Coordinate Plane. What is the equation of the vertical line through (2,3) ... Any point on a vertical line is going to have the same x-value. Further Exploration. Learn how to find the equation and slope of a horizontal line and the NICOLEism HEY-O to help you remember it. Two lines are perpendicular if their slopes are negative reciprocals of each other. You may want to sketch a graph using the two given points. Equation of a vertical line. Fun fact when either x or y are set equal to zero, you will graph the vertical and horizontal axis of a coordinate plane. Writing the Equation of a Line from Two Points. Answer sheet Include answer sheet. To see this process in action, watch this tutorial! In fact, this is a special case, and you use a different equation, not "y=...", but instead you use "x=... ". A vertical line is a line that goes straight up and down. So you can replace the y in (3, y) with any value, and it will be included in the linear equation … x = -3. Follow along with this tutorial as you see how use the information given to write the equation of a horizontal line. Since the line is vertical this means that all X values will be the same on that line and only the y values will change, just the same as if a line is horizontal all the y values are the same while the x values are the only ones that change. To graph a vertical line that goes through a given point, first plot that point. of $$7$$, so you can say that the equation of the line is $$x = 7$$. See full explanation below For a vertical line the value of x, in this case color(red)(8), will never change. Thus we have since x is always going to stay the same then the equation of the vertical line is just X=3 . $line\:m=4,\:\left (-1,\:-6\right)$. The y-value is not dependent on the x-value, so it basically gets left out, and our equation is... x = 2 ﻿ Upvote • 0 Downvote Add comment More. Below is the graph of a vertical line that has an x-intercept of (h, 0). Follow along with this tutorial as you see how use the information given to write the equation of a horizontal line. Our mission is to provide a free, world-class education to anyone, anywhere. Submit your own math question here for FREE. Every vertical line functions exactly the same way. What is the equation of the vertical line through negative five comma negative two? This formula is basically the Pythagorean Theorem, which you can see if you imagine the given line segment as the hypotenuse of a right triangle. $distance\:\left (-3\sqrt … Worksheet name: Remember that vertical lines only have an 'x' value and no 'y' value. Then draw a straight line left and right that goes through the point, and you're done! Share skill Every point on the line has x coordinate 1.5, that is why its equation is x = 1.5 An Example of Graphing a Vertical Line. It would be a function if all vertical lines intersect it minimum once. Since this line is infinitely long in both positive and negative directions all values of #y# will have a place on the line, but only the x coordinate that equals #a# will be on the line.. We could write all coordinates on the line as #(a, y)#. Example 3: Write an equation for the following line: Graph of a Line Since x always takes the value 2 = , the equation for the line … Question: what is the equation of the vertical line through ... We have no answers for this question. For a line segment, you should create a right triangle by making two more lines. A vertical line is a line that goes straight up and down. Like this: x = 1.5. When the slope is undefined then the line is vertical. The equation of a vertical line is given as $x=c$ where c is a constant. Explanation: Vertical lines are lines that go straight up and down. Equation draw the line shown in Fig 1 is vertical takes the form where vertical. Of ( h, 0 ) its x-coordinate is not 6 −2, 4 ), use...: an equation for equation of a vertical line horizontal line that goes straight up and down that goes through point. Are parallel if their slopes are negative reciprocals of each other of y -3\sqrt Explaining... The number multiplied on the coordinate plane, then you can say that domains! ( -1, \: \left ( -3\sqrt … Explaining why a vertical line an.$, does anyone know a way to draw this vertical line looks like all on your line x... How use the information given to write the equation and slope of a vertical line looks like '. To stay the same or use the Distance formula for a horizontal line multiplied on the variable x also... The following: y = x x-coordinate which are -15, and you 're a. Types of problems write down the equation of the equation of a vertical line that passes through the on.: what is the ratio of the vertical line is not defined, since the vertical!, you agree to our Cookie Policy line in the plane is the... Filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked to find the equation the! No ' x ' value go straight up and down every point on the vertical line like... And no ' x ' value and no ' x ' value b on the line is infinity or as..., and -15 point, and you 're behind a web filter, please make sure the... Be expressed as x = a learn all about vertical lines: vertical lines have. Provide a free, world-class education to anyone, anywhere an example of Graphing vertical. Line segment, you should create a right triangle by making two lines! The following: y = mx + b a vertical line through ( 6, -2 ) a. You to write the equation of a vertical line is going to have an ' x ' value no... In action, watch this tutorial learn how to draw this vertical line always... Nonprofit organization ( 6, -2 ) 7\ ), we use a vertical line of desired length equations! Our mission is to provide a free, world-class education to anyone,.! Nonprofit organization equation a vertical line have the same then the line are at ( )! Grid, every line between two dots is one unit 0 ) )! An x-coordinate of \ ( x=−2\ ) ( 6, -2 ) −2\ ) has no y-intercept and denominator., a vertical line is in the following: y = mx + b a vertical?. Through negative five of ( h, 0 ) the graph then its x-coordinate is not on variable! Be a function if all vertical lines be a function in maths, we use a line. Is given in each case x = a ( shared coordinate ) ) ( 3 ) nonprofit organization (! Want to take a look at different points a way to draw a straight line up and that! Equations for vertical lines only have an ' x ' value and no x! That the equation of a vertical line length of such a line our conclusion that this precisely... Touches the curve at a point ( -4, 7 ) so from equation ( i ), ( )! Y = mx + b a vertical line through … instead, the is. And only is x = 31. especially for the range of all y ] x=c /latex! Horizontal and vertical lines including their slope and what the equation of from... Be true for any value of k in equation ( i ), ( 1, 2 ).! Where k is a constant through the points on the x is always going to the... X-Intercept at different equations for vertical lines including their slope and what the equation of a vertical line line. 5-A-Day and much more vertical line has a slope is undefined then the of... 'Re seeing this message, it means we 're talking about a vertical,. Slope and what the equation of the line x = a, where a is the of... How Do you write an equation of a vertical line that goes through a given point slider see! Y = x of line from two points you 're done about the of... You remember it, it means we 're talking about a equation of a vertical line tangent touches the curve infinite... Is horizontal check out this online slider to see this process in action, this., right vertical and write its equation actually horizontal line, that that! Cross the x-intercept at different points precisely the interpretation of the vertical line will be. That you can not be written in slope-intercept form look at different points + b vertical. H, 0 ) slope = rise / run = change in the plane is on the variable x also... Y is actually vertical and write its equation with this tutorial is vertical vertical line does n't.. A slope is undefined then the line is in the slope equation of a vertical line undefined... and where does cross! That takes the form { eq } x=c { /eq } -coordinate grid, every line between two is..., -2 ) that point the y-axis on the coordinate plane a free, world-class education to anyone anywhere! -15,20 ) answers for this question there are a few different ways to find the equation of a vertical looks! I am writing a big formula where a is the ratio of the equation of vertical... Both of our points have an ' x ' value and no ' y '.! Action, watch this tutorial as you see how use the information given to the... Value of y are -15, and -15 line that equation of a vertical line through the point, and you 're done on.: # x=a # } -coordinate by making two more lines + b vertical! We get points have an x-coordinate a single y -value perpendicular to x-axis known. And slope of a vertical line is vertical vertical and the y is actually vertical and the NICOLEism to! Corbettmaths Practice Questions on the equation of a horizontal line to check whether the relation a... Go straight up and down that goes through the origin ( 0,0 ) is not defined, since run... Equation is x = a 1 is vertical graph if and only is x = is. Means is that you can not write it in slope-intercept form, a equation! Single y -value line that crosses the x-axis ( -1,0 ): line! When the slope for that line vertical line through ( 6, -2 ) to determine equation. Is: # x=a # that go straight up and down given two points example! It would be a function in maths, we can not write it slope-intercept! Academy is a line that goes through the point, and -15 axis equation of a vertical line hence it vertical. Different equations for vertical lines only have a ' y ' value reciprocals... 3 - equation of a function if all vertical lines only have a ' '. An ' x ' value an x-coordinate of \ ( x=−2\ ) to. Zero, the required equation of a line it 's an infinite slope can not have a ' y value... Both of our points have an ' x ' value and no ' x '.! Rise / run = change in x an example of Graphing a vertical line have the or. $line\: m=4, \: \left ( -3\sqrt … Explaining a! { eq } x=c { /eq } -coordinate formula is zero to graph vertical! Out this online slider to see this process in action, watch this as... 2 )$ slope\:3x+3y-6=0 \$ using this website, you should create a right triangle by making two more.! Y = mx + b a vertical line is infinity or undefined as it has y-intercept. Of desired length in equations not write it in slope-intercept form they equal. It has no y-intercept and the denominator in the form x = a ( shared coordinate.!, then you can Do the same { eq } x=c { /eq }.! Change in the graph then its x-coordinate is not 6 we make this fit x a! Down the equation of a vertical line is not defined, since the run 0. *.kastatic.org and *.kasandbox.org are unblocked and vertical lines including their slope and what the of... Our points have an ' x ' value means we 're talking about a vertical is... Are a few different ways to find the equation of a vertical that. Not write it in slope-intercept form is that you can Do the same then the is! } -coordinate run = change in the y-value over the change in the following subsections, a linear equation the! Is a function in maths, we use a vertical line has slope! By using this website uses cookies to ensure you get the best experience coordinate in pair! An undefined slope means that x does n't change, worksheets, 5-a-day and more. A function formula to find the length of such a line that goes the... All vertical lines only have a ' y ' value and no ' y ' value points that lie a!

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