Answer:
Explanation:
The first step is to find the equation of both lines. The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m is the slope
c is the y intercept. It is the value of y at the point where the line cuts the vertical axis.
The formula for calculating slope is expressed as
m = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of selected initial and final points on the line.
x1 and x2 are the x coordinates of the selected initial and final points on the line.
Considering labelled points on y = f(x),
when x1 = 0. y1 = - 3
when x2 = 2, y2 = 1
m = (1 - - 3)/(2 - 0) = 4/2 = 2
y intercept, c = - 3
The equation would be
y = f(x) = 2x - 3
Considering labelled points on y = g(x),
when x1 = 0. y1 = 6
when x2 = 2, y2 = - 2
m = (- 2 - 6)/(2 - 0) = - 8/2 = - 4
y intercept, c = 6
The equation would be
y = g(x) = - 4x + 6
The solution of both equations is the coordinate of the point of intersection. Thus,
Solution = (1.5, 0)
Given that
g(x) = kf(x), it means that
- 4x + 6 = k(2x - 3)
Substituting x = 1.5 into the equation, we have
- 4(1.5) + 6 = k(2 * 1.5) - 3
- 6 + 6 = 3k - 3
0 = 3k - 3
3k = 3
k = 3/3
k = 1