Can someone solve this problem?

a) your answer is 2086/14 =149 From integrating g(x) over the interval [-8, 6] and dividing by the interval length (14)

b)(-8,g(-8)) and (6,g(6)) correspond respectively to the points (-8, 569) and (6, 317);

writing the line equation that passes thru these 2 points is relatively straightforward.

[y1-y2] = m[x1-x2] and m = [y1-y2] / [x1-x2]. One valid equation for your line is

y = -18x + 425 [in the slope, y-intercept form that you requested]

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FWIW g(x) is a parabola (opening sharply upward) whose vertex (LOW point in this case) is (0, -7).

Integrating g(x) over the interval [-8, 6] gives you the area between the parab and the x-axis, where

area below the x-axis is treated as negative (area above is positive). A rectangle 149 x 14 would

have an area equal to the algebraic sum provided from the integral.