Question

10. The figure shows the graphs of the functions y = f(x) and y = g(x). The four indicated points all have integer coordinates.

Answer 1

Answer:

The value of k is -3.

Explanation:

To determine the value of k, first, find the equations of f(x) and g(x) using the two-point form of the equation of a line.

$\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}$

The indicated points on f(x) are (0,1) and (1,-1).

$\begin{gathered} \frac{y-1}{x-0}=\frac{-1-1}{1-0} \\ \frac{y-1}{x}=-\frac{2}{1} \\ y-1=-2x \\ f(x)=-2x+1 \end{gathered}$

Similarly, the indicated points on g(x) are (1,3) and (0,-3).

$\begin{gathered} \frac{y-3}{x-1}=\frac{-3-3}{0-1} \\ \frac{y-3}{x-1}=\frac{-6}{-1} \\ \frac{y-3}{x-1}=6 \\ y-3=6(x-1) \\ y-3=6x-6 \\ y=6x-6+3 \\ g(x)=6x-3 \end{gathered}$

Therefore, we have that:

$\begin{gathered} g(x)=kf(x) \\ 6x-3=-3(-2x+1)_{} \\ g(x)=-3f(x) \end{gathered}$

The value of k is -3.