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

What is the intersection point of the two straight lines 𝑦 − 1 = 0 and 𝑥 + 5 = 0?


Video Transcript

What is the intersection point of the two straight lines 𝑦 minus one equals zero and 𝑥 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 𝑦 or an 𝑥. When an equation of a straight line just has one variable, that means it will be either a horizontal or a vertical line. Let’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 𝑦 minus one equals zero, we could add one to both sides, giving us the equation 𝑦 equals one. In the second equation 𝑥 plus five equals zero, we would need to subtract five from both sides to give us 𝑥 equals negative five. In each of the cases of 𝑦 equals one and 𝑥 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, let’s think about how we would draw each of these straight lines. Let’s think about the line 𝑦 equals one. This means that for any ordered pair 𝑥, 𝑦, the 𝑦-value will always be one. So, any ordered pair with a 𝑦-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 𝑦 equals one, it will be a horizontal line, and the 𝑦-intercept indicates the constant in the term.

So, now we’ve drawn the line 𝑦 equals one, let’s see if we can draw the line of 𝑥 equals negative five. What this means is that in every ordered pair of 𝑥 and 𝑦, the 𝑥-value must be negative five and the 𝑦-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 𝑥 equals negative five.

Lines such as 𝑥 equals negative five will be vertical lines. And the 𝑥-intercept, or the place where it crosses the 𝑥-axis, will indicate the constant in the equation. And so, remembering that the line 𝑥 equals negative five is the same as the line 𝑥 plus five equals zero and the line 𝑦 equals one is the same as 𝑦 minus one equals zero, we’re asked for the intersection point of these two lines. And that will be at this point: negative five, one. And so, that’s our answer for the intersection of the lines 𝑦 minus one equals zero and 𝑥 plus five equals zero.

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