graph with y value of 11, -11 and x value of 9, -9
graph the proportional relationship y = -2x by plotting points

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 \( x \).

Learn how to graph the linear equation y = -2x by plotting key points within the range of x = -9 to 9 and y = -11 to 11. Understand the proportional relationship and slope-intercept form, ideal for students in Grades 6-8.

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