Question

A line with a slope of 1/4 passes through the points (9, -8) and (5, d). what is the value for?

Answer 1

        d + 8 = 1/4(x-9)
        d + 8 = 1/4x - 9/4
            - 8               - 8
    ------------------------------
        d = 1/4x - 17 

I just realized that this is not the answer you are looking for. It's an equation, not a value. Sorry about that.

Answer 2

Answer:
d = -9

Explanation:
The slope of the line can be calculated using the following formula:
slope = $\frac{y2-y1}{x2-x1}$

We are given:
slope = $\frac{1}{4}$
point (9,-8) representing (x1,y1)
point (5,d) representing (x2,y2)

Substitute with the givens in the above equation and solve for d as follows:
slope = $\frac{1}{4}$
$\frac{1}{4}$ = $\frac{d-(-8)}{5-9}$
$\frac{1}{4}$ = $\frac{d+8}{-4}$
4(d+8) = -4
d + 8 = -1
d = -1 - 8
d = -9

Hope this helps :)