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To graph the line \( y = 2x - 5 \), we follow these steps:

### Step-by-Step Explanation:

1. **Identify the slope and y-intercept**:
   - The equation is in slope-intercept form, \( y = mx + b \), where:
     - \( m = 2 \) (the slope), which means the line rises 2 units for every 1 unit it moves to the right.
     - \( b = -5 \) (the y-intercept), which is the point where the line crosses the y-axis.

2. **Plot the y-intercept**:
   - The y-intercept is \( (0, -5) \). This is the first point to plot on the graph. On the graph, locate 0 on the x-axis and go down to -5 on the y-axis.

3. **Use the slope to find another point**:
   - The slope \( m = 2 \) is written as \( \frac{2}{1} \). Starting from the point \( (0, -5) \), move 1 unit to the right (along the x-axis) and 2 units up (along the y-axis). This gives you a new point at \( (1, -3) \).

4. **Plot more points (optional)**:
   - To ensure accuracy, you can use the slope to find more points. From \( (1, -3) \), move another 1 unit to the right and 2 units up, which brings you to \( (2, -1) \).
   
5. **Draw the line**:
   - Once you have at least two points (preferably more), draw a straight line through them.

### Visual Verification:
If you'd like, I can help you with a digital sketch of the line based on the graph shown in your image. Does this solution make sense, or would you like me to provide more details or corrections?

### Related Questions:
1. How do you calculate the slope of a line given two points?
2. What is the significance of the y-intercept in a linear equation?
3. Can you convert a line equation from standard form to slope-intercept form?
4. How do you find the x-intercept of a line?
5. How would you graph a line with a negative slope?

**Tip:** Always remember that the slope describes the direction and steepness of a line.

Learn how to graph the linear equation y = 2x - 5. This solution provides a step-by-step explanation of plotting points using the slope and y-intercept. Perfect for Grades 7-9 students exploring algebraic concepts such as slope and graphing.

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