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The problem involves graphing the equation \( y = -\frac{4}{3}x \). You're asked to find the y-values corresponding to given x-values: \( x = -9, -6, -3, 0, 3, 6, \) and \( 9 \).

Let's calculate the y-values for each x-value using the equation \( y = -\frac{4}{3}x \).

1. **For \( x = -9 \):**
   \[
   y = -\frac{4}{3}(-9) = \frac{36}{3} = 12
   \]
2. **For \( x = -6 \):**
   \[
   y = -\frac{4}{3}(-6) = \frac{24}{3} = 8
   \]
3. **For \( x = -3 \):**
   \[
   y = -\frac{4}{3}(-3) = \frac{12}{3} = 4
   \]
4. **For \( x = 0 \):**
   \[
   y = -\frac{4}{3}(0) = 0
   \]
5. **For \( x = 3 \):**
   \[
   y = -\frac{4}{3}(3) = -\frac{12}{3} = -4
   \]
6. **For \( x = 6 \):**
   \[
   y = -\frac{4}{3}(6) = -\frac{24}{3} = -8
   \]
7. **For \( x = 9 \):**
   \[
   y = -\frac{4}{3}(9) = -\frac{36}{3} = -12
   \]

So, the corresponding y-values are:

- For \( x = -9 \), \( y = 12 \)
- For \( x = -6 \), \( y = 8 \)
- For \( x = -3 \), \( y = 4 \)
- For \( x = 0 \), \( y = 0 \)
- For \( x = 3 \), \( y = -4 \)
- For \( x = 6 \), \( y = -8 \)
- For \( x = 9 \), \( y = -12 \)

This set of points can now be plotted on a graph. The resulting graph should be a straight line with a negative slope, as expected from the equation \( y = -\frac{4}{3}x \).

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What does the slope of the line \( y = -\frac{4}{3}x \) indicate about the direction of the line?
2. How would the graph change if the equation were \( y = \frac{4}{3}x \) instead?
3. What is the y-intercept of the line \( y = -\frac{4}{3}x \)?
4. How can you determine the slope of a line from a graph?
5. What would be the equation of a line parallel to \( y = -\frac{4}{3}x \) but passing through a different point?

**Tip:** When dealing with linear equations, the coefficient of \( x \) gives you the slope, which tells you how steep the line is and in which direction it goes.

Graph the equation y = -4/3x. Let x = -9, -6, -3, 0, 3, 6, and 9. Find the following y-values. Then choose the correct graph of the equation.

This problem involves graphing the linear equation y = -4/3x by calculating the corresponding y-values for x-values of -9, -6, -3, 0, 3, 6, and 9. Learn how to plot these points on a graph and understand the negative slope of the line.

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