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 $x$.