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The image contains a set of linear equations, each paired with a blank graph. I will now explain how to graph each equation and the steps involved.

### Equation 29: \( y = -\frac{3}{4}x + 2 \)
- **Slope** = \( -\frac{3}{4} \): The line will decrease by 3 units vertically for every 4 units it moves to the right.
- **Y-intercept** = 2: The point where the line crosses the y-axis is at (0, 2).
- **Steps**:
  1. Start at (0, 2).
  2. From (0, 2), move down 3 units and right 4 units to plot another point at (4, -1).
  3. Draw a line through the points.

### Equation 30: \( y = \frac{2}{5}x + 5 \)
- **Slope** = \( \frac{2}{5} \): The line increases by 2 units for every 5 units to the right.
- **Y-intercept** = 5: The point where the line crosses the y-axis is (0, 5).
- **Steps**:
  1. Start at (0, 5).
  2. Move up 2 units and right 5 units to plot another point at (5, 7).
  3. Draw the line through these points.

### Equation 31: \( y = -\frac{4}{5}x - 1 \)
- **Slope** = \( -\frac{4}{5} \): The line decreases by 4 units for every 5 units to the right.
- **Y-intercept** = -1: The line crosses the y-axis at (0, -1).
- **Steps**:
  1. Start at (0, -1).
  2. Move down 4 units and right 5 units to plot a point at (5, -5).
  3. Draw the line through these points.

### Equation 32: \( y = -3x + 1 \)
- **Slope** = -3: The line decreases by 3 units for every 1 unit to the right.
- **Y-intercept** = 1: The line crosses the y-axis at (0, 1).
- **Steps**:
  1. Start at (0, 1).
  2. Move down 3 units and right 1 unit to plot another point at (1, -2).
  3. Draw the line through these points.

### Equation 33: \( y = 2x \)
- **Slope** = 2: The line increases by 2 units for every 1 unit to the right.
- **Y-intercept** = 0: The line passes through the origin (0, 0).
- **Steps**:
  1. Start at (0, 0).
  2. Move up 2 units and right 1 unit to plot a point at (1, 2).
  3. Draw the line through these points.

### Equation 34: \( y = 4 \)
- This is a horizontal line where \( y = 4 \), meaning the line passes through all points where the y-coordinate is 4.
- **Steps**:
  1. Plot a horizontal line across the graph at \( y = 4 \).

Would you like me to assist you with graphing any specific equation or provide further details on any part of this process?

### 5 related questions:
1. What is the significance of the slope and y-intercept in a linear equation?
2. How does a negative slope affect the direction of the line?
3. Can you explain how to identify whether a line is steep or shallow based on its slope?
4. What happens to the graph of a line if only the y-intercept changes?
5. How do horizontal and vertical lines differ in their equations?

### Tip:
Always start by plotting the y-intercept when graphing a linear equation, as it gives you the starting point for drawing the rest of the line.

How to graph the following linear equations: y = -3/4x + 2, y = 2/5x + 5, y = -4/5x - 1, y = -3x + 1, y = 2x, y = 4?

Learn how to graph linear equations like y = -3/4x + 2 and y = 2x with step-by-step instructions. Explore the concepts of slope and y-intercept to understand how lines are plotted on a coordinate plane. Suitable for Grade 8 students.

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