Question

The equation of line m is 4x+5y=−2.

Answer 1

$4x + 5y = - 2 \\ 5y = - 2 - 4x \\ y = \frac{ - 2}{5} - \frac{4x}{5}$
so the slope of the line m is a=-4/5
let a' be the slope of the line perpendicular to m ,
a.a'=-1 ( Perpendicular lines )

-4/5 x a'=-1
a'=
$\frac{ - 1}{ \frac{ - 4}{5} } = \frac{5}{4}$

Answer 2

The slope of a line that is perpendicular to line m is 5/4.

(I have taken the test and know that this is the correct answer.)