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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

Step-by-step explanation: