The problem here asks to consider the equation $y = 3x + 9$ and to plot the points corresponding to specific $x$-values: $x = -1$ and $x = 1$.

Step-by-Step Solution:

1. Substitute $x = -1$ into the equation $y = 3x + 9$: $y = 3(-1) + 9 = -3 + 9 = 6$ So, the point when $x = -1$ is $(-1, 6)$.

2. Substitute $x = 1$ into the equation $y = 3x + 9$: $y = 3(1) + 9 = 3 + 9 = 12$ So, the point when $x = 1$ is $(1, 12)$.

Plotting Points:

• The point $(-1, 6)$ should be plotted at $x = -1$ and $y = 6$.
• The point $(1, 12)$ should be plotted at $x = 1$ and $y = 12$.

These two points should align with the line defined by $y = 3x + 9$ if you connect them.

Would you like more details on how to plot these points or interpret linear equations?

Here are some further questions to expand your understanding:

1. What is the slope and y-intercept of the equation $y = 3x + 9$?
2. How would the line change if the equation was $y = 3x - 9$?
3. Can you find the y-coordinate for another value of $x$, say $x = 2$?
4. How does the slope of 3 affect the steepness of the line?
5. What does the y-intercept represent in the context of this line?

Tip: When plotting points, ensure you double-check coordinates by substituting values back into the equation to verify accuracy.