Question

the line $y = x$ is transformed into the line $y = 4x + 9$. fill in the blanks to describe the slope and $y-$intercept of the new line. the slope is steeper, and the line is shifted ? . downward upward

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. For the line $y=x$, we can rewrite it as $y = 1x+0$, so $m_1 = 1$ and $b_1=0$. For the line $y = 4x + 9$, $m_2=4$ and $b_2 = 9$.

Step2: Analyze the y - intercept change

The y - intercept of the original line ($y = x$) is $0$, and the y - intercept of the new line ($y=4x + 9$) is $9$. Since the y - intercept represents the point where the line crosses the y - axis ($x = 0$), when the y - intercept increases from $0$ to $9$, the line is shifted upward.

Answer:

upward