Question

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

Answer 1

Answer:

k=5

Step-by-step 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

Answer 2

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