Question

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k. Two lines labeled f(x) and g(x). Line f(x) passes through points (-4, 0) and (-3, 1). Line g(x) passes through points (-4, 0) and (-3, -3).

A.) 3
B.) 1/3
C.) -1/3
D.) −3

Answer 1

Option D.

Explanation:

If a line passing through two points, then the equation of line is

`(y-y_1)=(y_2-y_1)/(x_2-x_1)(x-x_1)`

It is given that Line f(x) passes through points (-4, 0) and (-3, 1). So, equation of line f(x) is

`(y-0)=(1-0)/(-3-(-4))(x-(-4))`

`y=1(x+4)`

So, function f(x) is

`f(x)=(x+4)` ...(1)

Line g(x) passes through points (-4, 0) and (-3, -3). So, equation of line f(x) is

`(y-0)=(-3-0)/(-3-(-4))(x-(-4))`

`y=-3(x+4)`

So, function g(x) is

`g(x)=-3(x+4)` ...(2)

Using (1) and (2), we get

`g(x)=-3f(x)` ...(3)

It is given that

`g(x)=kf(x)` ...(4)

On comparing (3) and (4), we get

`k=-3`

Therefore, the correct option is D.