# How do you write the equation using function notation that goes through (-2,-5); perpendicular to 3x + 5y = -17?

May 24, 2015

$3 x + 5 y = - 17$
can be written in slope-intercept form as
$y = - \frac{3}{5} x - 71$
which has a slope of $- \frac{3}{5}$

Any line perpendicular to this will have a slope $\frac{5}{3}$

A line going through $\left(- 2 , - 5\right)$ with a slope of $\frac{5}{3}$
is given by
$y + 5 = \frac{5}{3} \left(x + 2\right)$

$y = \frac{5 x}{3} + \frac{10}{3} - 5$

$y = \frac{5 x - 5}{3} = \frac{5}{3} \left(x - 1\right)$
or
$f \left(x\right) = \frac{5}{3} \left(x - 1\right)$