https://file.aiquickdraw.com/mathbot/file/1727217795116i3e32ki1.jpg

The equation you're asked to graph is \( y = x + 6 \). This is the equation of a straight line in slope-intercept form, \( y = mx + b \), where:

- \( m = 1 \) is the slope of the line.
- \( b = 6 \) is the y-intercept, which means the line crosses the y-axis at the point (0, 6).

### Steps to graph the equation:

1. **Plot the y-intercept**:
   - Start by marking the point (0, 6) on the y-axis, since \( b = 6 \).

2. **Use the slope to find another point**:
   - The slope \( m = 1 \) tells you to move 1 unit up and 1 unit to the right for each point. From (0, 6), go to (1, 7), then (2, 8), and so on.
   - Alternatively, you can go in the negative direction: move 1 unit down and 1 unit left, reaching (-1, 5), (-2, 4), etc.

3. **Draw the line**:
   - Connect all these points with a straight line.

### Verifying the graph:
- From the image, I can see a grid that is ready to be used for plotting. Start by marking the point (0, 6) on the y-axis, then follow the slope to place more points as described.

Would you like to discuss this further or need help with another problem?

### Follow-up questions:
1. What does the slope of 1 mean in this equation?
2. How would you graph \( y = 2x + 6 \)? 
3. If the equation was \( y = x - 3 \), how would the graph change?
4. How does changing the slope affect the steepness of the line?
5. Can you identify the x-intercept of this line?

**Tip**: Always start with the y-intercept and use the slope to determine how the line inclines or declines.

Learn how to graph the linear equation y = x + 6. This problem demonstrates graphing a straight line using the slope-intercept form, identifying the slope and y-intercept, and plotting points on the graph. Suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation