Question

122. Write the equation of the line that is

perpendicular to y = x-5 and passes through
the point (12,-1).

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`