Question

Which graph matches the linear equation: -2x + 3y = -6
A. (0, -4), (1, -10)
B. (0, 2), (1, -1)
C. (3, 0), (0, -2)
D. (1, 2), (0, -4)

Answer 1

To determine which graph matches the linear equation \(-2x + 3y = -6\), we can rewrite the equation in slope-intercept form \(y = mx + b\) or check if the given points satisfy the equation.

Let's express the equation in slope-intercept form:

1. Start with the original equation:
\[
-2x + 3y = -6
\]

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

Now we can check each of the answer options to see if the points satisfy the equation.

### Checking the options:

**A. (0, -4), (1, -10)**
- For (0, -4):
\[
y = \frac{2}{3}(0) - 2 = -2 \quad (\text{not } -4)
\]
- For (1, -10):
\[
y = \frac{2}{3}(1) - 2 = \frac{2}{3} - 2 = \frac{2}{3} - \frac{6}{3} = -\frac{4}{3} \quad (\text{not } -10)
\]

**B. (0, 2), (1, -1)**
- For (0, 2):
\[
y = \frac{2}{3}(0) - 2 = -2 \quad (\text{not } 2)
\]
- For (1, -1):
\[
y = \frac{2}{3}(1) - 2 = \frac{2}{3} - \frac{6}{3} = -\frac{4}{3} \quad (\text{not } -1)
\]

**C. (3, 0), (0, -2)**
- For (3, 0):
\[
0 = \frac{2}{3}(3) - 2 = 2 - 2 = 0 \quad (\text{correct})
\]
- For (0, -2):
\[
-2 = \frac{2}{3}(0) - 2 \quad (\text{correct})
\]
Both points satisfy the equation.

**D. (1, 2), (0, -4)**
- For (1, 2):
\[
2 = \frac{2}{3}(1) - 2 = \frac{2}{3} - 2 \quad (\text{not } 2)
\]
- For (0, -4):
\[
-4 = \frac{2}{3}(0) - 2 \quad (\text{not } -4)
\]

### Conclusion

The correct answer is **C. (3, 0), (0, -2)** as both points satisfy the equation \(-2x + 3y = -6\).