Question

Find the equation of the line perpendicular to y=−2 that passes through the point (4, −2).

Answer 1

x = 4

because it is perpendicular, the new equation has to be a vertical since the original was horizontal. We know that it passes through (4,-2) so it has to be x=4

Answer 2

Answer:

$x = 4$

Step-by-step explanation:

the line

$y=-2$

is a horizontal line on the -2 of the y-axis (for any x value, the y value is always -2).

Thus since $y=-2$ is a horizontal line, a perpendicular line to a horizontal line has to be a vertical line.

Now, we want this vertical to pass through the point:

$(4,-2)$.

This means that the only option we have is the line:

$x=4$

because this is the equation of a vertical line sitting on the x = 4.

This can be better visualized in the attached image. where the red line is$y = -2$ and the dotted blue line is $x = 4$