https://file.aiquickdraw.com/mathbot/file/1729504521054laqcnnxh.jpg

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.

For each ordered pair, decide if the ordered pair is a solution to the equation and if the point is on the line (Example equations: y = x + 2 and y = x - 4).

Check whether specific ordered pairs are solutions to the linear equations y = x + 2 and y = x - 4 by substituting values and verifying if the points lie on the line. A helpful guide for students in Grades 6-8 learning about linear equations and coordinate geometry.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation