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).

Step-by-step 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   

answer: what are the following choices

b

step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (0, 4) and (x₂, y₂ ) = (3, - 5) ← 2 points on the line

m = = = - 3

with m = - 3 and (a, b) = (3, - 5), then

y - (- 5) = - 3(x - 3), that is

y + 5 = - 3(x - 3) → b