Question

the line $y = x$ is transformed into the line $y = \frac{x}{5} + 9$. fill in the blanks to describe the slope and y-intercept of the new line. the slope is ? , and the line is shifted. flatter steeper

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.

Step2: Identify slope of new line

For the line $y=\frac{x}{5}+9$, comparing with $y = mx + b$, we can see that $m=\frac{1}{5}$.

Step3: Compare slopes for steepness

The original line is $y = x$, whose slope $m_1 = 1$. The new line has a slope $m_2=\frac{1}{5}$. Since $|\frac{1}{5}|=0.2<|1| = 1$, a smaller absolute value of the slope means the line is flatter.

Answer:

The slope is $\frac{1}{5}$, and the line is shifted flatter.