Question

21. 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 $y=-x-11$ 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 (9,2). Using the fomula

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

we get

$y-2=1(x-9) \iff y-2=x-9 \iff y=x-7$