Explanation:
the rate of change in an interval is always
( f (interval upper limit) - f (interval lower limit) ) /
(interval upper limit - interval lower limit)
31a.
( f (-2) - f (-4)) / (-2 - -4) = (-2 - -3) / 2 = 1/2
b.
( f (7) - f (3)) / (7 - 3) = (2.5 - 0.5) / 4 = 2/4 = 1/2
c.
yes, it is linear (= the function is a straight line), because it has the same change rate or slope everywhere.
32a.
f(x) = y = 35x + 75
b.
the slope is the factor of x, which is 35 for this function.
the slope is defined as "y coordinate change / x coordinate change" when going from one point on the line to another. and that is the same as the change rate, which is simply called slope for a line.
so, both are 35. it means for every increase of x by 1, y increases by 35.