Question

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)

Answer 1

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**: \( (3, 1), (0, -1) \).