Answer
$y= \frac52x + \frac12$
Work Step by Step
We are told to find the equation of the line that satisfies the following conditions:
Passes through the point (-1,-2), and perpendicular to the line $2x + 5y +8 = 0$
To find the equation of the line we must find the slope
then write it in the form:$ y =mx + b$
First solve the given equation for $y$:
$2x + 5y + 8 = 0$
$5y = -2x - 8$
$y = -\frac{2}{5}x - \frac{8}{5}$
Since the lines are perpendicular the slope is the negative reciprocal, so the slope of our equation is $m = \frac52$
$y - (-2) = \frac52(x-(-1)$
$y = \frac52x + \frac52 - 2$
$y= \frac52x + \frac12$
