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.