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Graph the linear equation

y = 2/3x - 1.
A. (-2, -2), (0, 1)
B. (1, 2), (0, -4
C. (1, -9), (0, -2)
D. (3, 1), (0, -1)

1 answer

To graph the linear equation \( y = \frac{2}{3}x - 1 \), we can find a couple of points by substituting values for \( x \) and solving for \( y \).

  1. Finding the y-intercept: Set \( x = 0 \): \[ y = \frac{2}{3}(0) - 1 = -1 \] So one point is \( (0, -1) \) (the y-intercept).

  2. Finding another point: Set \( x = 3 \): \[ y = \frac{2}{3}(3) - 1 = 2 - 1 = 1 \] So another point is \( (3, 1) \).

Now we can check which of the options contains these points:

  • Option A: \( (-2, -2), (0, 1) \) - Does not match.
  • Option B: \( (1, 2), (0, -4) \) - Does not match.
  • Option C: \( (1, -9), (0, -2) \) - Does not match.
  • Option D: \( (3, 1), (0, -1) \) - Both points match.

Thus, the correct option is D: \( (3, 1), (0, -1) \).