Math worksheet for graphing linear equations with slope-intercept form.

Problem Overview:

The task involves sketching the graph of each given linear equation and identifying its slope and y-intercept. The equations are provided in slope-intercept form: \( y = mx + b \), where:
- \( m \) is the slope,
- \( b \) is the y-intercept.

Solution Explanation:

For each equation, we will:
1. Identify the slope (\( m \)) and y-intercept (\( b \)).
2. Use these values to sketch the graph on the provided grid.
3. Verify the graph by plotting points or using the slope and y-intercept.

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Detailed Solutions for Each Equation:

#### 1. \( y = \frac{8}{3}x - 5 \)
- Slope (\( m \)): \( \frac{8}{3} \)
- y-intercept (\( b \)): \( -5 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, -5) \).
2. Use the slope \( \frac{8}{3} \):
- From \( (0, -5) \), move up 8 units and right 3 units to get another point.
- This gives the point \( (3, 3) \).
3. Draw a straight line through \( (0, -5) \) and \( (3, 3) \).

Graph: A line passing through \( (0, -5) \) with a steep positive slope.

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#### 2. \( y = -\frac{2}{5}x - 2 \)
- Slope (\( m \)): \( -\frac{2}{5} \)
- y-intercept (\( b \)): \( -2 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, -2) \).
2. Use the slope \( -\frac{2}{5} \):
- From \( (0, -2) \), move down 2 units and right 5 units to get another point.
- This gives the point \( (5, -4) \).
3. Draw a straight line through \( (0, -2) \) and \( (5, -4) \).

Graph: A line passing through \( (0, -2) \) with a gentle negative slope.

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#### 3. \( y = \frac{3}{2}x + 3 \)
- Slope (\( m \)): \( \frac{3}{2} \)
- y-intercept (\( b \)): \( 3 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, 3) \).
2. Use the slope \( \frac{3}{2} \):
- From \( (0, 3) \), move up 3 units and right 2 units to get another point.
- This gives the point \( (2, 6) \).
3. Draw a straight line through \( (0, 3) \) and \( (2, 6) \).

Graph: A line passing through \( (0, 3) \) with a moderate positive slope.

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#### 4. \( y = \frac{7}{4}x - 3 \)
- Slope (\( m \)): \( \frac{7}{4} \)
- y-intercept (\( b \)): \( -3 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, -3) \).
2. Use the slope \( \frac{7}{4} \):
- From \( (0, -3) \), move up 7 units and right 4 units to get another point.
- This gives the point \( (4, 4) \).
3. Draw a straight line through \( (0, -3) \) and \( (4, 4) \).

Graph: A line passing through \( (0, -3) \) with a steep positive slope.

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#### 5. \( y = \frac{1}{2}x + 3 \)
- Slope (\( m \)): \( \frac{1}{2} \)
- y-intercept (\( b \)): \( 3 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, 3) \).
2. Use the slope \( \frac{1}{2} \):
- From \( (0, 3) \), move up 1 unit and right 2 units to get another point.
- This gives the point \( (2, 4) \).
3. Draw a straight line through \( (0, 3) \) and \( (2, 4) \).

Graph: A line passing through \( (0, 3) \) with a gentle positive slope.

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#### 6. \( y = -3x - 3 \)
- Slope (\( m \)): \( -3 \)
- y-intercept (\( b \)): \( -3 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, -3) \).
2. Use the slope \( -3 \):
- From \( (0, -3) \), move down 3 units and right 1 unit to get another point.
- This gives the point \( (1, -6) \).
3. Draw a straight line through \( (0, -3) \) and \( (1, -6) \).

Graph: A line passing through \( (0, -3) \) with a steep negative slope.

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#### 7. \( y = -x + 4 \)
- Slope (\( m \)): \( -1 \)
- y-intercept (\( b \)): \( 4 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, 4) \).
2. Use the slope \( -1 \):
- From \( (0, 4) \), move down 1 unit and right 1 unit to get another point.
- This gives the point \( (1, 3) \).
3. Draw a straight line through \( (0, 4) \) and \( (1, 3) \).

Graph: A line passing through \( (0, 4) \) with a negative slope of \( -1 \).

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#### 8. \( y = 3x + 2 \)
- Slope (\( m \)): \( 3 \)
- y-intercept (\( b \)): \( 2 \)

Steps to Sketch:
1. Start at the y-intercept: \( (0, 2) \).
2. Use the slope \( 3 \):
- From \( (0, 2) \), move up 3 units and right 1 unit to get another point.
- This gives the point \( (1, 5) \).
3. Draw a straight line through \( (0, 2) \) and \( (1, 5) \).

Graph: A line passing through \( (0, 2) \) with a steep positive slope.

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Final Answer:

The slopes and y-intercepts for each equation are already filled in the image. The graphs are sketched based on these values.

\[
\boxed{
\begin{array}{ll}
1) & \text{slope } = \frac{8}{3}, \text{ y-intercept } = -5 \\
2) & \text{slope } = -\frac{2}{5}, \text{ y-intercept } = -2 \\
3) & \text{slope } = \frac{3}{2}, \text{ y-intercept } = 3 \\
4) & \text{slope } = \frac{7}{4}, \text{ y-intercept } = -3 \\
5) & \text{slope } = \frac{1}{2}, \text{ y-intercept } = 3 \\
6) & \text{slope } = -3, \text{ y-intercept } = -3 \\
7) & \text{slope } = -1, \text{ y-intercept } = 4 \\
8) & \text{slope } = 3, \text{ y-intercept } = 2 \\
\end{array}
}
\]