The value of k is 3
Solution:
Let us first find the equation of the line f(x).
The points on the line are (-6, -2) and (0, 4).
Here, [tex]x_1=-6, y_1=-2, x_2=0, y_2=4[/tex]
Formula to find equation of a line:
[tex]$\frac{y-y_1}{x-x_1} =\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]$\frac{y-(-2)}{x-(-6)} =\frac{4-(-2)}{0-(-6)}[/tex]
[tex]$\frac{y+2}{x+6} =\frac{4+2}{6}[/tex]
[tex]$\frac{y+2}{x+6} =\frac{1}{1}[/tex]
Do cross multiplication.
y + 2 = x + 6
y = x + 4
f(x) = x + 4
Given that g(x) = f(kx)
g(x) = kx + 4
The point in the graph of g(x) is ( -2, -2).
g(-2) = k(-2) + 4
we know that g(-2) = -2.
-2 = -2k + 4
Subtract 4 from both sides.
-6 = -2k
Divide by -2 on both sides.
3 = k
k = 3
The value of k is 3.
