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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 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

Respuesta :

calculista

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

[tex]m=(2-0)/(-2+4)\\m=1[/tex]

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=1\\(-4,0)[/tex]

substitute

[tex]y-0=(1)(x+4)[/tex]

[tex]y=x+4)[/tex]

Remember that

f(x)=y

so

[tex]f(x)=x+4[/tex]

step 2

Find the equation of the line g(x)

we have the points

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

Find the slope m

[tex]m=(10-0)/(-2+4)\\m=5[/tex]

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=5\\(-4,0)[/tex]

substitute

[tex]y-0=(5)(x+4)[/tex]

[tex]y=5(x+4)[/tex]

Remember that

g(x)=y

so

[tex]g(x)=5(x+4)[/tex]

Remember that

[tex]g(x)=kf(x)[/tex] ------> [tex]g(x)=5(x+4)[/tex]

therefore

k=5

Answer:

k=5

Step-by-step 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

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