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Graph the equation y equals negative two thirds x

. Let x equals negative 9 comma negative 6​, minus3​, ​0, 3​, 6​, and 9.
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Part 1
Find the following​ y-values. Then choose the correct graph of the equation to the right.

1 answer

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.