How to Write Equations for the Vertical & the Horizontal Lines Passing Through the Point

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Equations for the vertical and horizontal lines passing through a point need to be written in a very specific way. Find out how to write equations for the vertical and horizontal lines passing through a point with help from a longtime math teacher in this free video clip.

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Video Transcript

Hi, my name is Marija and I'm a mathematician. And today, I'm going to show you how to write the equation of vertical and horizontal lines that pass through a point. So, if you are given a point, two, three, and we want to know the equation of the vertical and horizontal line. So, first, we'll look at the vertical line that passes through that point. So, I'm going to draw my coordinate plane, with my X axis being the horizontal line, and my Y axis being the vertical line. And go to the point, one, two, one, two, three, so here's my point. To draw a vertical line that goes through that point, I'm drawing a line that's parallel to the Y-axis. So, here's my vertical line. Now, what I notice is that this is the point, two, three and if I plot any other point on this line. For example, this is the point, two, four, this is the point, two, five, two, six and so on. What I notice, is that my X coordinate is constantly two. So, the equation for the vertical line that passes through that point, is that X is a constant, and that constant is two. So, the equation here is X equals two. Now, for the horizontal line that passes through this point, I'm going to draw a line that is parallel to my X-axis. And what I notice here, is that the Y coordinate now, will always be consistent. So, for example, this point here is two, three, this one here is one, three, this is zero, three, this is negative one, three. So, my Y coordinate is consistent, it's always going to be three. So, the equation for the horizontal line is going to be Y equals three. So, for horizontal lines, your Y coordinate is consistent, your equation is going to be Y equals a constant. And for your vertical lines, the X coordinates is going to be the one that's constant. So, your equation is going to be,Y equals a constant. And for your vertical lines, the X coordinates is going to be the one that's constant. So your equation will be X equals a constant, that constant being whatever the coordinate is. So, that's how you write equations for vertical and horizontal lines, that pass through a given point.

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