Answer:
(d) y -8 = -5/8(x +8)
Explanation:
You want the point-slope equation for the line through the points listed in the table.
Point-slope form
The point-slope form of the equation for a line is ...
y -k = m(x -h) . . . . . . . line with slope m through point (h, k)
Application
The first point listed in the table is (h, k) = (-8, 8), so the equation will be of the form ...
y -8 = m(x -(-8))
y -8 = m(x +8)
Comparing this form to the answer choices, we see that it matches choices (b) and (d). These have m = -8/5 and m = -5/8, respectively.
Slope
The slope of the line is given by the formula ...
m = (y2 -y1)/(x2 -x1)
m = (4 7/8 -8)/(-3 -(-8)) = (-3 1/8)/5
Clearly the magnitude of this is less than 1, so cannot match m=-8/5, which has a magnitude greater than 1. The appropriate answer choice is (d):
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Additional comments
The slope can be worked out to be ...
(-3 1/8)/5 = (-25/8)/5 = -5/8
This confirms our answer choice.
We know the magnitude of (-3 1/8)/5 is less than 1 because 3 1/8 < 5.