Answer:
Value of k = -2
Step-by-step explanation:
Using slope intercept form:
The equation of line is given by:
y = mx+b
where, m is the slope and b is the y-intercept.
As per the statement:
The graphs of y = f(x) and y = g(x) are shown on the coordinate plane.
First find f(x):
Consider two points on y=f(x) are:
(0,-3) and (2, 1)
Formula for slope:
then;
then;
Substitute the point (0, -3) to solve for b:
⇒
∴
Similarly for g(x):
Consider two points on y = g(x) are:
(0, 6) and (2, -2)
then;
then;
then;
Substitute the points (0, 6) to solve for b:
⇒
then we get an equation:
y = g(x) = -4x+6
It is given that: If g(x) = k* f(x)
Solve for k:
⇒
on comparing both sides we have;
⇒
Divide both sides by -2 we have;
or
-3k = 6
⇒k = -2
Therefore, the value of k is, -2