first for the slope you do rise over run. Meaning you find a point on the graph intersects "cleanly" as in (-2,-4) then find another point on the graph where the line intersects (3,-2). to find the slope you do the change in Y over the Change in X so what that means is that tou would take one Y value and subtract it from the otherY value (from the two points you just found) so in this example (-4)-(-2) which equals -2. then you do the same process for the X values (make sure to start with the same point) so (-2)-(3) which equals -5. then you divide (or leave as a fraction in this case) -2/-5 which simplifies to 2/5. so The slope is 2/5.
A line that is perpendicular to it has a slope that is an opposite reciprocal, which in this case is -1/3. Now you use point slope form which is y-y1=m(x-x1) that would be y+5=-1/3(x-6). Distribute the -1/3 and get y+5= -1/3 x+ 2. Subtract 5 from both sides and get y=-1/3 x - 3