Question

timmy writes the equation $f(x) = \frac{1}{4}x - 1$. he then doubles both of the terms on the right side to create the equation $g(x) = \frac{1}{2}x - 2$. how does the graph of $g(x)$ compare to the graph of $f(x)$?
○ the line of $g(x)$ is steeper and has a higher y-intercept.
○ the line of $g(x)$ is less steep and has a lower y-intercept.
○ the line of $g(x)$ is steeper and has a lower y-intercept.
○ the line of $g(x)$ is less steep and has a higher y-intercept.

Explanation:

Step1: Compare slopes (steepness)

The slope of $f(x)$ is $\frac{1}{4}$, and the slope of $g(x)$ is $\frac{1}{2}$. Since $\frac{1}{2} > \frac{1}{4}$, $g(x)$ is steeper.

Step2: Compare y-intercepts

The y-intercept of $f(x)$ is $-1$, and the y-intercept of $g(x)$ is $-2$. Since $-2 < -1$, $g(x)$ has a lower y-intercept.

Answer:

The line of $g(x)$ is steeper and has a lower y-intercept.