Question

Given f(x) and g(x) = k⋅f(x), use the graph to determine the value of k.

Two lines labeled f of x and g of x. Line f of x passes through points negative 4, 0 and negative 2, 2. Line g of x passes through points negative 4, 0 and negative 2, negative 10.

-5
-1/5
1/5
5

Answer 1

Answer: -5 just because the guy ontop said it was

Answer 2

k = -5

Explanation:

The function f(x) passes through the points (-4,0) and (-2,2).

Therefore, the equation of the straight line is given by

`(y-2)/(2-0) =(x-(-2))/(-2-(-4))`

⇒
`(y-2)/(2) =(x+2)/(2)`

⇒ y = x + 4

⇒ f(x) = x + 4 ......... (1)

Now, g(x) passes through the points (-4,0) and (-2,-10).

Then the equation will be

`(y-(-10))/(-10-0) =(x-(-2))/(-2-(-4))`

⇒
`(y+10)/(-10) =(x+2)/(2)`

⇒ y = - 5x - 20 = - 5 (x + 4)

⇒ g(x) = -5 (x + 4) ....... (2)

Therefore, from equations (1) and (2) we get k = -5 (Answer)