Question

Which ordered pairs represent points on the graph of this equation? Select all that apply.

2/3 y = - 1/2 x

Answer 1

To determine which ordered pairs represent points on the graph of the equation \( \frac{2}{3}y = -\frac{1}{2}x \), we can rearrange the equation into a more familiar form, if needed, or simply plug in the \( x \) and \( y \) values from the provided ordered pairs to check if they satisfy the equation.

First, let's rearrange the equation for easier calculation:

1. Multiply both sides by 6 to eliminate the fractions:
\[
6 \left(\frac{2}{3}y\right) = 6 \left(-\frac{1}{2}x\right)
\]
This simplifies to:
\[
4y = -3x
\]

2. Now, let's express \( y \):
\[
y = -\frac{3}{4}x
\]

Now, if you have specific ordered pairs (like (x, y) points), substitute the \( x \) values into this equation to check if the corresponding \( y \) values match.

For example, if we check these pairs:

1. \( (0, 0) \):
- Substitute: \( y = -\frac{3}{4}(0) = 0 \) → Point is (0, 0) on the graph.

2. \( (4, -3) \):
- Substitute: \( y = -\frac{3}{4}(4) = -3 \) → Point is (4, -3) on the graph.

3. \( (8, -6) \):
- Substitute: \( y = -\frac{3}{4}(8) = -6 \) → Point is (8, -6) on the graph.

4. \( (2, 1) \):
- Substitute: \( y = -\frac{3}{4}(2) = -1.5 \) → Point is not (2, 1) on the graph.

Continue this process for any pairs you have in mind.

Please list the ordered pairs that you're checking, and I can help verify which ones are on the graph of the equation given!