The point (3; -2) lies on the graph of y=-2x+4 . Draw the graph of y = -2x +4

To graph the equation \( y = -2x + 4 \), follow these steps:

1. **Identify the slope and intercept**:
   - The equation is in the slope-intercept form \( y = mx + b \), where:
     - \( m = -2 \) is the slope, meaning the line decreases by 2 units vertically for every 1 unit it moves horizontally.
     - \( b = 4 \) is the y-intercept, meaning the line crosses the y-axis at \( (0, 4) \).

2. **Plot the y-intercept**:
   - Start by plotting the point \( (0, 4) \) on the graph.

3. **Use the slope to find another point**:
   - From \( (0, 4) \), use the slope \( -2 \) (which is \( -\frac{2}{1} \)) to go down 2 units and move 1 unit to the right.
   - This will give the point \( (1, 2) \).
   
4. **Plot the point (3, -2)**:
   - You know from the problem that the point \( (3, -2) \) lies on the line. Plot this point to confirm that it matches the line.

5. **Draw the line**:
   - Connect the points \( (0, 4) \), \( (1, 2) \), and \( (3, -2) \) with a straight line. This is the graph of \( y = -2x + 4 \).

Would you like me to generate a visual graph for you?

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Here are 5 relative questions to expand on this:
1. What is the general form of a linear equation?
2. How do you interpret the slope of a line geometrically?
3. How would the graph change if the slope were positive?
4. What happens to the graph if the y-intercept is negative?
5. How can you verify if a point lies on a given line algebraically?

**Tip:** Always remember that the slope controls the steepness and direction of a line—whether it rises or falls!

The point (3; -2) lies on the graph of y=-2x+4. Draw the graph of y = -2x +4

Learn how to graph the linear equation y = -2x + 4. This problem covers key concepts such as slope, intercepts, and graphing a line using the slope-intercept form. Suitable for students in Grades 8-10, this tutorial walks you through the process step-by-step, including plotting points like (3, -2).

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