https://file.aiquickdraw.com/mathbot/file/17296367180980yes4a5w.jpg

The equation given in the problem is:

\[
y = 4x + 2
\]

We need to check which of the ordered pairs \((-2, -6)\), \((-1, 0)\), \((-2, 6)\), and \((0, 2)\) satisfy this equation.

### 1. For \((-2, -6)\):
Substitute \(x = -2\) into the equation:
\[
y = 4(-2) + 2 = -8 + 2 = -6
\]
Since the calculated \(y = -6\) matches the given \(y = -6\), this pair is a **solution**.

### 2. For \((-1, 0)\):
Substitute \(x = -1\) into the equation:
\[
y = 4(-1) + 2 = -4 + 2 = -2
\]
Since the calculated \(y = -2\) does not match the given \(y = 0\), this pair is **not a solution**.

### 3. For \((-2, 6)\):
Substitute \(x = -2\) into the equation:
\[
y = 4(-2) + 2 = -8 + 2 = -6
\]
Since the calculated \(y = -6\) does not match the given \(y = 6\), this pair is **not a solution**.

### 4. For \((0, 2)\):
Substitute \(x = 0\) into the equation:
\[
y = 4(0) + 2 = 0 + 2 = 2
\]
Since the calculated \(y = 2\) matches the given \(y = 2\), this pair is a **solution**.

### Final Answer:
- \((-2, -6)\) is a solution.
- \((-1, 0)\) is not a solution.
- \((-2, 6)\) is not a solution.
- \((0, 2)\) is a solution.

Would you like more details, or do you have any questions?

Here are 5 related questions to consider:
1. How can we determine solutions for inequalities rather than equations?
2. What happens if we change the slope in the equation \(y = 4x + 2\)?
3. How do we graph linear equations like \(y = 4x + 2\)?
4. What is the effect of changing the constant in the equation \(y = 4x + 2\)?
5. Can there be no solution for some ordered pairs for a linear equation?

**Tip:** When solving linear equations with ordered pairs, always check by substituting both the \(x\)- and \(y\)-values into the equation.

Decide which of the ordered pairs are solutions for the equation y = 4x + 2.

Learn how to check if ordered pairs are solutions for the linear equation y = 4x + 2. Follow step-by-step substitution to verify if (-2, -6), (-1, 0), (-2, 6), and (0, 2) satisfy the equation.

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