On rural highways, the average speed S (in miles per hour) is related to the amount of curvature C (in degrees) of the road. Suppose that on a straight road (C = 0), the average speed is 47.5 miles per hour and this decreases by 0.65 mph for each additional degree of curvature. Find the formula expressing S as a linear function of C.
A)S = 0.65C + 47.5
B)S = 47.5C + 0.65
C)S = 47.5C - 0.65
D)S = -0.65C + 47.5

Question

On rural highways, the average speed S (in miles per hour) is related to the amount of curvature C (in degrees) of the road. Suppose that on a straight road (C = 0), the average speed is 47.5 miles per hour and this decreases by 0.65 mph for each additional degree of curvature. Find the formula expressing S as a linear function of C.
A)S = 0.65C + 47.5 
B)S = 47.5C + 0.65 
C)S = 47.5C - 0.65 
D)S = -0.65C + 47.5

Quizplus · Accepted Answer

Since the average speed decreases by 0.65 mph for each additional degree of curvature, we need to multiply the amount of curvature (C) by -0.65 to get the decrease in speed. This means the formula expressing S as a linear function of C is of the form S = mC + b, where m is the slope (change in speed divided by change in curvature) and b is the y-intercept (the average speed on a straight road). Plugging in the given values, we get S = -0.65C + 47.5, which corresponds to option D.

On Rural Highways, the Average Speed S (In Miles Per