Answer
$y=-\frac{8}{5}(x)+9$
Work Step by Step
RECALL:
(1) The point-slope form of a line's equation is $y-y_1=m(x-x_1)$ where $m$=slope and $(x_1, y_1)$ is a point on the line.
(2) The slope-intercept form of a line's equation is $y=mx+b$ where $m$=slope and $b$ is the y-coordinate of the line's y-intercept.
(3) Parallel lines have equal slopes.
(4) Perpendicular lines have slopes whose product is $-1$ (negative reciprocals of each other).
The line is perpendicular to $y=\frac{5}{8}x-2$. Since the slope of this line is $\frac{5}{8}$, then the slope of the line perpendicular to it is the negative reciprocal of $\frac{5}{8}$, which is $-\frac{8}{5}$.
Using the given point on the line $(0, 9)$ (which is the y-intercept) and the slope $-\frac{8}{5}$, the equation of the line in slope-intercept form is:
$y=-\frac{8}{5}x+9$
