## Calculus 8th Edition

$y= \frac52x + \frac12$
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 $m = \frac52$ $y - (-2) = \frac52(x-(-1)$ $y = \frac52x + \frac52 - 2$ $y= \frac52x + \frac12$