To graph the equation \( y = 2x - 3 \), follow these steps:

1. **Identify the slope and y-intercept:**
   - The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
   - Here, the slope \( m = 2 \) and the y-intercept \( b = -3 \).

2. **Plot the y-intercept:**
   - Start by plotting the point where the line crosses the y-axis. This occurs at \( (0, -3) \).

3. **Use the slope to find another point:**
   - The slope \( 2 \) means that for every 1 unit you move to the right (positive direction along the x-axis), you move 2 units up (positive direction along the y-axis).
   - Starting from \( (0, -3) \), move 1 unit to the right to \( (1, -3) \), and then 2 units up to \( (1, -1) \). Plot this point at \( (1, -1) \).

4. **Draw the line:**
   - Connect the two points \( (0, -3) \) and \( (1, -1) \) with a straight line.
   - Extend the line in both directions.

5. **Label the graph:**
   - Make sure to label the x-axis and y-axis and write the equation \( y = 2x - 3 \) on the graph.

This is what the graph should look like:

- A line that crosses the y-axis at \( (0, -3) \) and moves upward with a slope of 2.

Would you like me to generate a visual graph of this line?

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Here are 5 related questions:

1. How would the graph change if the slope were \( \frac{1}{2} \) instead of 2?
2. What would happen to the graph if the y-intercept were \( +3 \) instead of \( -3 \)?
3. How do you find the x-intercept of the line \( y = 2x - 3 \)?
4. What is the significance of the slope in a linear equation?
5. How would you graph the line if the equation were \( y = -2x + 3 \)?

**Tip:** Understanding the slope-intercept form of a linear equation can help you quickly graph any linear equation.

Learn how to graph the linear equation y=2x-3 with detailed steps and examples. This guide covers plotting the y-intercept, using the slope to find points, drawing the line, and labeling the graph effectively. Suitable for students in Grades 7-9.

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