# Question Video: Finding the Point of Intersection between Horizontal and Vertical Lines Mathematics

What is the intersection point of the two straight lines π¦ β 1 = 0 and π₯ + 5 = 0?

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### Video Transcript

What is the intersection point of the two straight lines π¦ minus one equals zero and π₯ plus five equals zero?

So, here we have two straight lines, and notice that in each of these straight lines, we just have one variable, either a π¦ or an π₯. When an equation of a straight line just has one variable, that means it will be either a horizontal or a vertical line. Letβs take each of these equations of the lines and see if we can make the variable the subject of the equation.

In the equation π¦ minus one equals zero, we could add one to both sides, giving us the equation π¦ equals one. In the second equation π₯ plus five equals zero, we would need to subtract five from both sides to give us π₯ equals negative five. In each of the cases of π¦ equals one and π₯ equals negative five, we still have equations of a straight line. And both of these will correspond to the original straight line equations we were given.

So, letβs think about how we would draw each of these straight lines. Letβs think about the line π¦ equals one. This means that for any ordered pair π₯, π¦, the π¦-value will always be one. So, any ordered pair with a π¦-value of one would lie on this straight line. For example, the coordinate or ordered pair of zero, one would be on the line, so would three, one; five, one; and even negative five, one. When we have a line like π¦ equals one, it will be a horizontal line, and the π¦-intercept indicates the constant in the term.

So, now weβve drawn the line π¦ equals one, letβs see if we can draw the line of π₯ equals negative five. What this means is that in every ordered pair of π₯ and π¦, the π₯-value must be negative five and the π¦-value can be anything. So, negative five, zero would lie on this line, so would negative five, three; negative five, five; and even negative five, negative four. Joining these up, we can see how we can create the line π₯ equals negative five.

Lines such as π₯ equals negative five will be vertical lines. And the π₯-intercept, or the place where it crosses the π₯-axis, will indicate the constant in the equation. And so, remembering that the line π₯ equals negative five is the same as the line π₯ plus five equals zero and the line π¦ equals one is the same as π¦ minus one equals zero, weβre asked for the intersection point of these two lines. And that will be at this point: negative five, one. And so, thatβs our answer for the intersection of the lines π¦ minus one equals zero and π₯ plus five equals zero.