which of the following is an ordered pair of the relation y = -2/3x + 6

To find an ordered pair from the relation given by the equation \( y = -\frac{2}{3}x + 6 \), we can choose a value for \( x \) and then calculate the corresponding value of \( y \).

Let's choose \( x = 0 \):

\[ y = -\frac{2}{3}(0) + 6 = 6 \]

So, one ordered pair from the relation is \( (0, 6) \).

You can choose other values for \( x \) as well to find different ordered pairs. For example, if we let \( x = 3 \):

\[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \]

This gives us another ordered pair \( (3, 4) \).

In summary, some ordered pairs from the relation \( y = -\frac{2}{3}x + 6 \) include \( (0, 6) \) and \( (3, 4) \). If you have specific options listed, please provide them, and I can help determine which one is an ordered pair from the relation.

Let's evaluate each of the provided ordered pairs using the equation \( y = -\frac{2}{3}x + 6 \) to determine which one is valid.

1. For \( (1, 4) \): \[ y = -\frac{2}{3}(1) + 6 = -\frac{2}{3} + 6 = -\frac{2}{3} + \frac{18}{3} = \frac{16}{3} \neq 4 \] This pair is not valid.

2. For \( (0, -\frac{2}{3}) \): \[ y = -\frac{2}{3}(0) + 6 = 6 \neq -\frac{2}{3} \] This pair is not valid.

3. For \( (3, 4) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \] This pair is valid.

4. For \( (3, 8) \): \[ y = -\frac{2}{3}(3) + 6 = -2 + 6 = 4 \neq 8 \] This pair is not valid.

Based on the evaluations, the only ordered pair that satisfies the relation \( y = -\frac{2}{3}x + 6 \) is (3, 4).

Yes, let's double-check the calculations to ensure everything is correct.

The equation we're working with is: \[ y = -\frac{2}{3}x + 6 \]

Now, we will evaluate each provided ordered pair again:

1. For \( (1, 4) \): \[ y = -\frac{2}{3}(1) + 6 \ y = -\frac{2}{3} + 6 \ y = -\frac{2}{3} + \frac{18}{3} \ y = \frac{16}{3} \quad \text{(this is approximately 5.33, not 4)} \] Not valid.

2. For \( (0, -\frac{2}{3}) \): \[ y = -\frac{2}{3}(0) + 6 \ y = 6 \quad \text{(not -2/3)} \] Not valid.

3. For \( (3, 4) \): \[ y = -\frac{2}{3}(3) + 6 \ y = -2 + 6 \ y = 4 \quad \text{(this matches)} \] Valid.

4. For \( (3, 8) \): \[ y = -\frac{2}{3}(3) + 6 \ y = -2 + 6 \ y = 4 \quad \text{(not 8)} \] Not valid.

From this double-checking, I confirm that the only ordered pair that satisfies the equation \( y = -\frac{2}{3}x + 6 \) is indeed (3, 4). Thank you for your patience!