Question

This is the graph of the equation y = 3x + 2.
Which ordered pairs are solutions to the equation? Select all that apply.
(-6, 1)
(1,5)
(-5, -3)
(-1,-1)
(3, 2)
(-2,-4)

Answer 1

To determine which ordered pairs are solutions to the equation \( y = 3x + 2 \), we can plug in the x-values from each ordered pair into the equation and see if the corresponding y-value is produced.

1. For the point \((-6, 1)\):
\[
y = 3(-6) + 2 = -18 + 2 = -16 \quad \text{(not a solution)}
\]

2. For the point \((1, 5)\):
\[
y = 3(1) + 2 = 3 + 2 = 5 \quad \text{(is a solution)}
\]

3. For the point \((-5, -3)\):
\[
y = 3(-5) + 2 = -15 + 2 = -13 \quad \text{(not a solution)}
\]

4. For the point \((-1, -1)\):
\[
y = 3(-1) + 2 = -3 + 2 = -1 \quad \text{(is a solution)}
\]

5. For the point \((3, 2)\):
\[
y = 3(3) + 2 = 9 + 2 = 11 \quad \text{(not a solution)}
\]

6. For the point \((-2, -4)\):
\[
y = 3(-2) + 2 = -6 + 2 = -4 \quad \text{(is a solution)}
\]

Therefore, the ordered pairs that are solutions to the equation \( y = 3x + 2 \) are:

- \((1, 5)\)
- \((-1, -1)\)
- \((-2, -4)\)