Question

The linear function f(x) has a slope of "5 and a y - intercept of 1. The linear function g(x) passes through the points (-4, 2) and (2, 14). Which statement is true?

A. The y-intercept of f(x) is 9 units larger than the y-intercept of g(x).

B. The y-intercept of g(x) is 9 units larger than the y-intercept of f(x).

C. The y-intercept of f(x) is 7 units larger than the y-intercept of g(x).

D. The y-intercept of g(x) is 7 units larger than the y-intercept of f(x).

Answer 1

Explanation:

f(x) = 5x + 1

Given these two points on the graph of g(x), we must determine the slope, m, of the line. Going from (-4, 2) to (2, 14), x (the run) increases by 6 and y (the rise) increases by 12, so the slope is m = rise/run = 12/6, or m = 2. Adapting the slope-intercept form y = mx + b, we find b as follows:

14 = 2(2) + b, or 14 = 4 + b, or b = 10. Then g(x) is 2x + 10.

Comparing f(x) = 5x + 1, we determine whether each of the four statements is true or false:

A is false; the respective y-intercepts of f and g are 1 and 10.

B is true: the respective y-intercepts of g and f are 10 and 1.

C is false; neither y-intercept is 7.

D is false. 1