Question

the line y = x is transformed into the line y = 8x - 3. 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 $y = 8x-3$, comparing with $y=mx + b$, we see that $m = 8$. So the slope of the new line is 8.

Step3: Compare slopes for steepness

The original line is $y=x$, which has a slope of $m_1 = 1$. The new line has a slope of $m_2=8$. Since $|8|>|1|$, a larger absolute value of the slope means the line is steeper. Also, for the $y$-intercept, in $y = 8x-3$, the $y$-intercept $b=- 3$, which means the line is shifted down by 3 units (compared to $y = x$ which has a $y$-intercept of 0). But for the slope part, the slope is 8 and the line is steeper.

Answer:

The slope is $\boldsymbol{8}$, and the line is shifted $\boldsymbol{\text{steeper}}$ (and also shifted down by 3 units for the $y$-intercept part, but focusing on the slope - related steepness here).