The equation you provided is a linear equation in slope-intercept form, \( y = mx + b \), where:

- \( m \) is the slope of the line, which represents the rate of change.
- \( b \) is the y-intercept, where the line crosses the y-axis.

In your equation, \( y = x + 6 \):
- The slope \( m = 1 \) (since there is an implicit 1 in front of \( x \)).
- The y-intercept \( b = 6 \).

### Key Points:
- The slope tells us that for every 1 unit increase in \( x \), \( y \) increases by 1.
- The line crosses the y-axis at the point \( (0, 6) \).

### Graphing the Line:
- Start at \( (0, 6) \) on the y-axis.
- Move 1 unit to the right and 1 unit up (because of the slope 1).
- Repeat this to plot more points and draw the straight line through them.

Would you like a more detailed explanation or a graph of this equation?

Here are some questions you might want to explore next:
1. What happens if you change the slope of the line?
2. How does the y-intercept affect the graph?
3. Can you find the x-intercept of this line?
4. How would you write the equation if the line were steeper?
5. How can you convert this equation into standard form?

**Tip**: To find the x-intercept of a line, set \( y = 0 \) and solve for \( x \).

Discover how to solve and graph the linear equation y = x + 6. Learn about slope-intercept form, the slope of the line (m = 1), and the y-intercept (b = 6). This example helps students understand how to interpret and plot linear equations. Suitable for Grades 6-8.

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