To graph the proportional relationship $y = -2x$, we'll use the given equation to calculate and plot specific points within the range of $x = 9$, $x = -9$, $y = 11$, and $y = -11$.

Steps:

1. Identify the equation: $y = -2x$ is a linear equation with a slope of $-2$ and a y-intercept at $(0, 0)$.

2. Choose x-values: To plot, we can select a few $x$-values and calculate their corresponding $y$-values: $x = -9, -5, -3, 0, 3, 5, 9$

3. Calculate corresponding y-values: Plugging into $y = -2x$:

   • When $x = -9$, $y = -2(-9) = 18$ (but 18 exceeds the $y = 11$ limit).
   • When $x = -5$, $y = -2(-5) = 10$.
   • When $x = -3$, $y = -2(-3) = 6$.
   • When $x = 0$, $y = 0$.
   • When $x = 3$, $y = -2(3) = -6$.
   • When $x = 5$, $y = -2(5) = -10$.
   • When $x = 9$, $y = -2(9) = -18$ (but $-18$ exceeds the $y = -11$ limit).

4. Plot points: The points to plot on the graph are: $(-5, 10), (-3, 6), (0, 0), (3, -6), (5, -10)$ You can draw a straight line through these points, as the relationship is linear.

If you want me to generate a visual graph for you, I can plot these points and draw the line. Would you like me to do that?

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Questions:

1. What is the effect of changing the slope in the equation $y = -2x$?
2. How do the points differ if the equation changes to $y = 2x$?
3. Can you describe how to find the slope from the equation $y = -2x$?
4. How would you interpret the intercept in this linear equation?
5. What is the domain and range for this linear equation given the constraints?

Tip: The slope of a line tells you how much $y$ changes for every unit change in $x$.