Question

the line $y = x$ is transformed into the line $y = 2x + 3$. 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 original line $y=x$, we can rewrite it as $y = 1x+0$, so $m_1 = 1$ and $b_1=0$. For the new line $y = 2x + 3$, $m_2=2$ and $b_2 = 3$.

Step2: Analyze Y - Intercept Shift

The y - intercept of a line represents the point where the line crosses the y - axis (when $x = 0$). The original y - intercept is $0$ (from $y=x$) and the new y - intercept is $3$ (from $y = 2x+3$). Since the y - intercept has increased from $0$ to $3$, the line is shifted upward.

Answer:

upward