Question

how does the slope of $g(x)$ compare to the slope of $f(x)$?○ the slope of $g(x)$ is the opposite of the slope of $f(x)$.○ the slope of $g(x)$ is less than the slope of $f(x)$.○ the slope of $g(x)$ is greater than the slope of $f(x)$.○ the slope of $g(x)$ is equal to the slope of $f(x)$.graph of linear functions $f(x)$ and $g(x)$ on a coordinate plane

Explanation:

Step1: Calculate slope of $f(x)$

Use two points on $f(x)$: $(-2,0)$ and $(0,1)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\text{Slope of } f(x)=\frac{1-0}{0-(-2)}=\frac{1}{2}$

Step2: Calculate slope of $g(x)$

Use two points on $g(x)$: $(-4,0)$ and $(0,2)$. Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}$
$\text{Slope of } g(x)=\frac{2-0}{0-(-4)}=\frac{2}{4}=\frac{1}{2}$

Step3: Compare the two slopes

Both slopes equal $\frac{1}{2}$.

Answer:

The slope of $g(x)$ is equal to the slope of $f(x)$.