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

Option D.

Step-by-step explanation:

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

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

So, function f(x) is

   ...(1)

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

So, function g(x) is

   ...(2)

Using (1) and (2), we get

   ...(3)

It is given that

    ...(4)

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

Therefore, the correct option is D.