Question

Question was provided via image upload.

Explanation:

Step1: Analyze Graph 5

The graph is a horizontal line. For a horizontal line, the slope \( m = 0 \) (since \( m=\frac{y_2 - y_1}{x_2 - x_1} \) and \( y \)-values are constant). The line crosses the \( y \)-axis at \( y = 2 \) (assuming the grid: looking at the \( y \)-coordinate, the line is at \( y = 2 \)? Wait, no, looking at the first graph (5), the horizontal line is at \( y = 2 \)? Wait, the grid: the \( y \)-axis has marks. Wait, maybe it's \( y = 2 \)? Wait, no, let's check the coordinates. The horizontal line: for any \( x \), \( y \) is constant. Let's see the \( y \)-intercept. The line is at \( y = 2 \)? Wait, maybe I misread. Wait, the first graph (5) has a horizontal line. Let's assume the \( y \)-intercept is \( b = 2 \)? Wait, no, maybe it's \( y = 2 \)? Wait, no, let's look again. The first graph (5): the horizontal line is at \( y = 2 \)? Wait, the \( y \)-axis: the top part, the line is horizontal. Let's say the equation is \( y = 2 \) (since it's horizontal, slope 0, \( y \)-intercept 2).

Step2: Analyze Graph 6

The graph is a line with negative slope. Let's find two points. Let's take \( (0, 2) \) and \( (4, 0) \). Then slope \( m=\frac{0 - 2}{4 - 0}=\frac{-2}{4}=-\frac{1}{2} \). \( y \)-intercept \( b = 2 \). So equation \( y = -\frac{1}{2}x + 2 \).

Step3: Analyze Graph 7

The graph is a line with positive slope. Let's take two points: \( (-4, -1) \) and \( (0, 0) \)? Wait, no. Wait, the line passes through \( (-4, -1) \) and \( (0, 0) \)? Wait, no, let's check. The line goes through \( (-4, -1) \) and \( (4, 1) \)? Wait, slope \( m=\frac{1 - (-1)}{4 - (-4)}=\frac{2}{8}=\frac{1}{4} \). \( y \)-intercept \( b = 0 \)? Wait, no, when \( x = 0 \), \( y = 0 \)? Wait, the line passes through the origin? Wait, no, looking at graph 7: the line crosses the \( y \)-axis at \( (0, 0) \)? Wait, maybe points \( (-4, -1) \) and \( (0, 0) \): slope \( \frac{0 - (-1)}{0 - (-4)}=\frac{1}{4} \). So equation \( y=\frac{1}{4}x \).

Step4: Analyze Graph 8

The graph is a line with positive slope. Let's take \( (-2, -1) \) and \( (0, 3) \)? Wait, no. Wait, points \( (-2, -1) \) and \( (0, 3) \)? No, let's take \( (-2, -1) \) and \( (0, 3) \)? Wait, no, better points: \( (-2, -1) \) and \( (0, 3) \)? No, let's look at graph 8: the line passes through \( (-2, -1) \) and \( (0, 3) \)? Wait, no, maybe \( (-2, -1) \) and \( (0, 3) \): slope \( \frac{3 - (-1)}{0 - (-2)}=\frac{4}{2}=2 \). \( y \)-intercept \( b = 3 \)? Wait, no, when \( x = 0 \), \( y = 3 \)? Wait, the line in graph 8: let's take \( (-2, -1) \) and \( (0, 3) \), slope 2, \( y \)-intercept 3. So equation \( y = 2x + 3 \).

Step5: Analyze Graph 9

The graph is a vertical line. Vertical lines have undefined slope. The line is at \( x = 3 \) (since it's vertical, passing through \( x = 3 \)). So equation \( x = 3 \).

Step6: Analyze Graph 10

The graph is a line with negative slope, passing through the origin. Let's take \( (0, 0) \) and \( (1, -2) \). Slope \( m=\frac{-2 - 0}{1 - 0}=-2 \). So equation \( y = -2x \).

(Note: Since the question was not specified, I assumed analyzing the equations of the lines. If the question was different, please clarify.)

Answer:

For Graph 5: \( y = 2 \) (slope 0, \( y \)-intercept 2)
For Graph 6: \( y = -\frac{1}{2}x + 2 \) (slope \( -\frac{1}{2} \), \( y \)-intercept 2)
For Graph 7: \( y = \frac{1}{4}x \) (slope \( \frac{1}{4} \), \( y \)-intercept 0)
For Graph 8: \( y = 2x + 3 \) (slope 2, \( y \)-intercept 3)
For Graph 9: \( x = 3 \) (vertical line, undefined slope)
For Graph 10: \( y = -2x \) (slope -2, \( y \)-intercept 0)