Question

Graph the equation y equals negative two thirds x
. Let x equals negative 9 comma negative 6​, minus3​, ​0, 3​, 6​, and 9.
Question content area bottom left
Part 1
Find the following​ y-values. Then choose the correct graph of the equation to the right.

Answer 1

Let's calculate the \(y\)-values for each given \(x\) value using the equation \(y = -\frac{2}{3}x\).

1. For \(x = -9\):
\[
y = -\frac{2}{3}(-9) = \frac{18}{3} = 6
\]

2. For \(x = -6\):
\[
y = -\frac{2}{3}(-6) = \frac{12}{3} = 4
\]

3. For \(x = -3\):
\[
y = -\frac{2}{3}(-3) = \frac{6}{3} = 2
\]

4. For \(x = 0\):
\[
y = -\frac{2}{3}(0) = 0
\]

5. For \(x = 3\):
\[
y = -\frac{2}{3}(3) = -2
\]

6. For \(x = 6\):
\[
y = -\frac{2}{3}(6) = -4
\]

7. For \(x = 9\):
\[
y = -\frac{2}{3}(9) = -6
\]

Now we have the following points to plot based on the \(x\) values and the corresponding \(y\) values:

- \((-9, 6)\)
- \((-6, 4)\)
- \((-3, 2)\)
- \((0, 0)\)
- \((3, -2)\)
- \((6, -4)\)
- \((9, -6)\)

### Summary of Points:
- \( (-9, 6) \)
- \( (-6, 4) \)
- \( (-3, 2) \)
- \( (0, 0) \)
- \( (3, -2) \)
- \( (6, -4) \)
- \( (9, -6) \)

Once you have all these points, you can plot them on a graph and draw a straight line through them to represent the equation \(y = -\frac{2}{3}x\). This line will have a negative slope, indicating it decreases as \(x\) increases.

If you're choosing a graph representation, look for a straight line that passes through all of the calculated points above.