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

k=5

Explanation:

Find the equation of the line f(x)

we have the points

(-4,0) and (-2,2)

Find the slope m

Find the equation of the line in point slope form

we have

substitute

Remember that

f(x)=y

so

step 2

Find the equation of the line g(x)

we have the points

(-4,0) and (-2,-10)

Find the slope m

Find the equation of the line in point slope form

we have

substitute

Remember that

g(x)=y

so

Remember that

------>

therefore

k=5

Answer 2

k=5

Explanation:

step 1

Find the equation of the line f(x)

we have the points

(-4,0) and (-2,2)

Find the slope m

`m=(2-0)/(-2+4)\\m=1`

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=1\\(-4,0)`

substitute

`y-0=(1)(x+4)`

`y=x+4)`

Remember that

f(x)=y

so

`f(x)=x+4`

step 2

Find the equation of the line g(x)

we have the points

(-4,0) and (-2,-10)

Find the slope m

`m=(10-0)/(-2+4)\\m=5`

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=5\\(-4,0)`

substitute

`y-0=(5)(x+4)`

`y=5(x+4)`

Remember that

g(x)=y

so

`g(x)=5(x+4)`

Remember that

`g(x)=kf(x)` ------>
`g(x)=5(x+4)`

therefore

k=5