Answer
y=-2.5x+4
Work Step by Step
Since they are supposed to be perpendicular, the desired line must have a slope that is the opposite of the reciprocal of the slope of the given line, -2x+5y=35:
-2x+5y=35
5y=2x+35
y=$\frac{2}{5}$x+7.
When changed to slope intercept form, we can see that the slope of the given line has a slope of $\frac{2}{5}$. Therefore, the slope of the desired line must have a slope of m=-$\frac{5}{2}$ or 2.5.
y-y$_1$=m(x-x$_1$)
y-9=-2.5(x+2)
y-9=-2.5x-5
y=-2.5x+4
