For these exercises, the goal is to check whether each ordered pair is a solution to the given linear equation and determine if the point lies on the graph of the line.

For exercise 5:

The equation is $y = x + 2$.

You are given the ordered pairs:

• A: (0, 2)
• B: (1, 2)
• C: (-1, 1)
• D: (-3, -1)

To check if each point is on the line, substitute the $x$-value into the equation and see if the resulting $y$-value matches the given $y$-value of the point.

1. For A: (0, 2), substitute $x = 0$ into $y = x + 2$: $y = 0 + 2 = 2 \quad \text{(True, A is on the line)}$

2. For B: (1, 2), substitute $x = 1$: $y = 1 + 2 = 3 \quad \text{(False, B is not on the line)}$

3. For C: (-1, 1), substitute $x = -1$: $y = -1 + 2 = 1 \quad \text{(True, C is on the line)}$

4. For D: (-3, -1), substitute $x = -3$: $y = -3 + 2 = -1 \quad \text{(True, D is on the line)}$

For exercise 6:

The equation is $y = x - 4$.

The ordered pairs are:

• A: (0, -4)
• B: (3, -1)
• C: (2, 2)
• D: (1, -5)

1. For A: (0, -4), substitute $x = 0$: $y = 0 - 4 = -4 \quad \text{(True, A is on the line)}$

2. For B: (3, -1), substitute $x = 3$: $y = 3 - 4 = -1 \quad \text{(True, B is on the line)}$

3. For C: (2, 2), substitute $x = 2$: $y = 2 - 4 = -2 \quad \text{(False, C is not on the line)}$

4. For D: (1, -5), substitute $x = 1$: $y = 1 - 4 = -3 \quad \text{(False, D is not on the line)}$

Summary:

• For exercise 5, points A, C, and D are on the line.
• For exercise 6, points A and B are on the line.

Would you like more details or explanations on any part of this solution?

Follow-up Questions:

1. What general method can you use to determine if a point is on a line?
2. How does changing the slope of a line affect the position of points on the graph?
3. What happens to a line's graph when you change the y-intercept?
4. How would you find the equation of a line if you're given two points?
5. How does graphing an equation help in solving a system of equations?

Tip: When checking if a point is on a line, always plug in the x-value of the point into the equation and compare the computed y-value with the point's y-value.