math question I don't understand

Question

Write the equation of the line that passes through the points (4,-5)(4,−5) and (4,-7)(4,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.

Answer 1

Hello Bobbi,

Look at the two points (4,-5) and (4,-7). They have the same x-coordinate. Therefore, the only kind of line that can go through those two points is a vertical line. Specifically, it’s the line x = 4.

(you can draw the points on a coordinate grid to help you visualize their positions)

Another way to figure it out is finding the slope using the formula (y2-y1)/(x2-x1). Here that slope is -2/0 which is undefined, which indicates a vertical line.

Answer 2

(4,-5) and (4,-7) have a vertical line through them: x=4

it might help to plot the two points and connect them with a line. It's one point above the other. It's a vertical line, as vertical as it gets.