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

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erinna erinna · Answer 1 · 2020-06-14T08:45:27+02:00

Answer:

Option D.

Step-by-step explanation:

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

[tex](y-y_1)=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]

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

[tex](y-0)=\dfrac{1-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=1(x+4)[/tex]

So, function f(x) is

[tex]f(x)=(x+4)[/tex] ...(1)

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

[tex](y-0)=\dfrac{-3-0}{-3-(-4)}(x-(-4))[/tex]

[tex]y=-3(x+4)[/tex]

So, function g(x) is

[tex]g(x)=-3(x+4)[/tex] ...(2)

Using (1) and (2), we get

[tex]g(x)=-3f(x)[/tex] ...(3)

It is given that

[tex]g(x)=kf(x)[/tex] ...(4)

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

[tex]k=-3[/tex]

Therefore, the correct option is D.