The graphs of y = f(x) and y = g(x) are shown on the coordinate plane below. If g(x) = k* f(x), what is the value of k?

step 1
find the equation of f(x)
points
(2,1)  and (0,-3)
m=(y2-y1)/(x2-x1)----------> m=(-3-1)/(0-2)---------> m=2
y-y1=m(x-x1)-----> y+3=2*(x-0)------> y=2x-3
f(x)=2x-3

step 2
find the equation of g(x)
points 
(0,6)  and (2,-2)
m=(y2-y1)/(x2-x1)----------> m=(-2-6)/(2-0)---------> m=-4
y-y1=m(x-x1)-----> y-6=-4*(x-0)------> y=-4x+6
g(x)=-4x+6

step 3
find the value of k
If g(x) = k* f(x)
so
-4x+6=k*[2x-3]-------> -4x+6=2kx-3k
-4x=2kx--------> k=-2
6=-3k------------> k=-2

the answer is 
k=-2