Question

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

Answer 1

the answers are:

(1 , 4)

( 0 , -2/3)

(3 , 4)

(3 , 8)

Answer 2

you sure

Answer 3

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.

Answer 4

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)**.

Answer 5

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!