Answer:
Option A k=5
Step-by-step explanation:
step 1
Find the equation of f(x)
we have the points
(-10,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+10)=1[/tex]
The function in slope intercept form is equal to
[tex]f(x)=mx+b[/tex]
we have
[tex]m=1[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]f(x)=x+4[/tex]
step 2
Find the equation of g(x)
we have the points
(-2,-6) and (0,4)
Find the slope m
[tex]m=(4+6)/(0+2)=5[/tex]
The function in slope intercept form is equal to
[tex]g(x)=mx+b[/tex]
we have
[tex]m=5[/tex]
[tex]b=4[/tex] -----> the point (0,4) is the y-intercept
substitute
[tex]g(x)=5x+4[/tex]
step 3
Find the value of k
we have
[tex]f(x)=x+4[/tex]
[tex]g(x)=5x+4[/tex] -----> equation A
[tex]g(x)=f(kx)[/tex] -----> equation B
[tex]f(kx)=kx+4[/tex] ----> equation C
substitute equation A and equation C in equation B and solve for k
[tex]kx+4=5x+4[/tex]
[tex]kx-5x=0\\kx=5x\\k=5[/tex]
