timmy writes the equation $f(x)=\frac{1}{4}x - 1$. he then doubles both of the terms on the right side to…

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 $f(x)$?\no the line of $g(x)$ is steeper and has a higher y - intercept.\no the line of $g(x)$ is less steep and has a lower y - intercept.\no the line of $g(x)$ is steeper and has a lower y - intercept.\no the line of $g(x)$ is less steep and has a higher y - intercept.

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 $f(x)$?\no the line of $g(x)$ is steeper and has a higher y - intercept.\no the line of $g(x)$ is less steep and has a lower y - intercept.\no the line of $g(x)$ is steeper and has a lower y - intercept.\no the line of $g(x)$ is less steep and has a higher y - intercept.

Answer

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. For $f(x)=\frac{1}{4}x - 1$, the slope $m_1=\frac{1}{4}$ and the y - intercept $b_1=-1$. For $g(x)=\frac{1}{2}x - 2$, the slope $m_2=\frac{1}{2}$ and the y - intercept $b_2=-2$.

Step2: Compare slopes

The larger the absolute value of the slope, the steeper the line. Since $\left|\frac{1}{2}\right|>\left|\frac{1}{4}\right|$, the line of $g(x)$ is steeper than the line of $f(x)$.

Step3: Compare y - intercepts

We have $b_1=-1$ and $b_2 = - 2$. Since $-1>-2$, the y - intercept of $f(x)$ is higher than the y - intercept of $g(x)$, or the y - intercept of $g(x)$ is lower.

Answer:

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