The equation of line q is y = -5/9x + 8. Line r is perpendicular to q. What is the slope of
line r?

These are not the exact numbers but just plug in the numbers of yours Because we know that q is a perpendicular line to p we know that its slope is the negative reciprocal of the slope of p. So its slope is 7/10. Now we just need to find its y-intercept. To do that we write what we know about line q. So we know that the equation for line q looks like:

y = (7/10)x + b

We also know that q passes through the point (8,7), so we now plug that in and solve for b:

7 = (7/10)(8) + b
7 - (56/10) = b
(70/10) - (56/10) = b
14/10 = 7/5 = b

So now that we have solved for the y-intercept, we know that the equation for line q is:

y = (7/10)x + 7/5

The slope of the function is 0.5.