Question

122. Write the equation of the line that is

Answer 1

When a line is given in the form

$y=mx+q$

The slope of the line is m. So, in this case, the slope of $y=x-5$ is 1.

Given a slope $m$, you find the slope of a perpendicular line $m'$ by imposing

$m\cdot m' = -1$

So, if the given line has slope 1, a perpendicular line has slope $m'$ given by

$1 \cdot m' = -1$

and thus $m'=-1$

So, we want a line with slope -1 and passing through (12,-1). Using the fomula

$y-y_0=m(x-x_0)$

we get

$y-(-1)=-1(x-12) \iff y+1=-x+12 \iff y=-x+11$