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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

User Tzortzik
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1 Answer

4 votes

Answer:

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.

User Dizzyf
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6.9k points