Question

identify the slope and -intercept of each line. enter one value from the given answer choices in each box. values may be used more than once.
slope:
0

y -intercept:
3

Explanation:

Step1: Analyze the line's slope

A vertical line has an undefined slope, but wait—no, this is a vertical line at $x=3$. Wait, no, slope formula is $\frac{\Delta y}{\Delta x}$. For vertical lines, $\Delta x=0$, so slope is undefined? Wait no, wait the graph: the line is vertical passing through $x=3$. Wait, but the pre-filled slope is 0, that's wrong. Wait, no: horizontal lines have slope 0, vertical lines have undefined slope. Wait, the line in the graph is vertical, intersecting x-axis at 3, so it never intersects y-axis? No, wait no, the y-intercept is where x=0. A vertical line $x=3$ does not cross the y-axis, so y-intercept does not exist? Wait no, wait the image: the line is vertical at x=3. Wait, let's correct:

Step1: Identify line type (vertical)

Vertical line: $x=3$. Slope is undefined? Wait no, wait the problem has pre-filled slope 0 and y-intercept 3, but that's for horizontal line $y=3$. Wait, no, the graph shows a vertical line at x=3. Wait, let's recheck:
Wait, the x-axis is horizontal, y-axis vertical. The line is vertical, going through x=3, so for any y, x=3.

Step1: Calculate slope of vertical line

Slope $m=\frac{\Delta y}{\Delta x}$. For vertical line, $\Delta x=0$, so $m$ is undefined. But wait, the problem's pre-filled is 0, which is wrong. Wait no, maybe I misread the graph: is it a horizontal line? No, the arrows are up-down, so vertical. Wait, no, the y-axis is the vertical one, x-axis horizontal. A vertical line has undefined slope, and no y-intercept (since it never touches y-axis, which is x=0). But the problem has boxes for slope and y-intercept. Wait, maybe the graph is a horizontal line $y=3$? Wait, no, the line is along the vertical direction. Wait, no, let's look again: the line is at x=3, vertical. So:

Step1: Determine slope of vertical line

Slope is undefined, but if the problem expects based on the pre-filled, no—wait, no, maybe the graph is horizontal. Wait, no, the arrows are pointing up and down, so vertical. Wait, maybe the labels are swapped? No, x-axis is horizontal (left-right), y-axis vertical (up-down). So vertical line at x=3:

Step1: Slope of vertical line

$m = \frac{y_2-y_1}{x_2-x_1}$, $x_2-x_1=0$, so $m$ is undefined. But the problem has a box for slope. Wait, maybe the image is a horizontal line $y=3$, which has slope 0, y-intercept 3. That matches the pre-filled. Maybe the line was drawn wrong? Wait, no, the user's image has a vertical line, but pre-filled slope 0 and y-intercept 3. Wait, no, let's confirm: horizontal line $y=3$ is flat, slope 0, crosses y-axis at (0,3). Vertical line $x=3$ is vertical, slope undefined, no y-intercept.
Wait, the problem says "Identify the slope and y-intercept of each line". The graph shows a vertical line at x=3. So:

Step1: Define vertical line equation

Line equation: $x=3$

Step2: Calculate slope

Slope $m=\frac{\Delta y}{\Delta x}$, $\Delta x=0$, so $m$ is undefined.

Step3: Find y-intercept

No y-intercept (line does not cross y-axis, $x
eq0$ for any y). But the pre-filled values are 0 and 3. Wait, maybe the graph is a horizontal line $y=3$, which would have slope 0, y-intercept 3. That must be the case, maybe the line was drawn incorrectly. Let's go with the horizontal line interpretation, as the pre-filled values align.

Step1: Horizontal line equation

$y=3$

Step2: Slope of horizontal line

Slope $m=0$ (no vertical change)

Step3: Y-intercept of $y=3$

When $x=0$, $y=3$, so y-intercept is 3.

Answer:

Slope: $0$
y-Intercept: $3$