Question

Which ordered pairs represent points on the graph of this equation?
–6x–5y=5

Answer 1

To determine which ordered pairs represent points on the graph of the equation \(-6x - 5y = 5\), we can test various pairs \((x, y)\) by substituting them into the equation and checking if the equation holds true.

Let's solve for \(y\) in terms of \(x\) to make it easier to check ordered pairs:

\[
-6x - 5y = 5
\]
Add \(6x\) to both sides:

\[
-5y = 6x + 5
\]
Now divide by \(-5\):

\[
y = -\frac{6}{5}x - 1
\]

Now, we can test different pairs. Here are a few examples:

1. **Test the point (0, -1)**:
\[
y = -\frac{6}{5}(0) - 1 = -1 \quad \text{(true)}
\]
\((0, -1)\) is on the graph.

2. **Test the point (1, -2)**:
\[
y = -\frac{6}{5}(1) - 1 = -\frac{6}{5} - \frac{5}{5} = -\frac{11}{5} \quad \text{(false)}
\]
\((1, -2)\) is not on the graph.

3. **Test the point (-1, 1)**:
\[
y = -\frac{6}{5}(-1) - 1 = \frac{6}{5} - 1 = \frac{1}{5} \quad \text{(false)}
\]
\((-1, 1)\) is not on the graph.

4. **Test the point (2, -3)**:
\[
y = -\frac{6}{5}(2) - 1 = -\frac{12}{5} - \frac{5}{5} = -\frac{17}{5} \quad \text{(false)}
\]
\((2, -3)\) is not on the graph.

5. **Test the point (-1, 1)**:
\[
-6(-1) - 5(1) = 6 - 5 = 1 \quad \text{(false)}
\]
\((-1, 1)\) is not on the graph.

6. **Test the point (-1, -1)**:
\[
-6(-1) - 5(-1) = 6 + 5 = 11 \quad \text{(false)}
\]
\((-1, -1)\) is not on the graph.

If you have specific ordered pairs you need checked, please provide them, and I can confirm their validity against the equation!