The slope of g(x) is (-2-6)/(2-0)=-8/2=-4 and we can see from (0,6) that 6 is the y-intercept so:
g(x)=-4x+6
The slope of f(x) is (1--3)/(2-0)=4/2=2 and we can see from (0,-3) that -3 is the y-intercepts so:
f(x)=2x-3
g(x)=k*(f(x))
k=g(x)/f(x) using the lines that we found we have:
k=(-4x+6)/(2x-3) factoring the numerator we see:
k=-2(2x-3)/(2x-3) so the (2x-3)s cancel out leaving:
k=-2
