https://file.aiquickdraw.com/mathbot/file/1722717632985mamqnalc.jpg

Graph the equations on the same set of axes and find the coordinates of the point of intersection. x + y = 5          y =  3x-7

To determine the correct point of intersection for the given equations \(x + y = 5\) and \(y = 3x - 7\) using the provided graph, we can follow these steps:

1. **Verify the point of intersection algebraically:**
   - From the previous solution, we know the intersection point algebraically:
     \[
     \begin{aligned}
     &\text{Set } y = 5 - x \text{ equal to } y = 3x - 7: \\
     &5 - x = 3x - 7 \\
     &5 + 7 = 3x + x \\
     &12 = 4x \\
     &x = 3 \\
     &y = 5 - 3 = 2 \\
     &\text{So, the point of intersection is } (3, 2).
     \end{aligned}
     \]

2. **Compare the given options with the algebraic solution:**
   - **Option A: (3, 2)**
   - **Option B: \(\left(\frac{5}{4}, \frac{15}{4}\right)\)**
   - **Option C: (-6, 11)**

The correct algebraic solution is (3, 2), which corresponds to **Option A**.

To further verify, let's examine the graphs:

- The point (3, 2) should be where the lines intersect.
- Check the given graphs in the image:

### Analysis of the Graphs:
- **Option A:**
  - The intersection point (3, 2) seems accurate according to our algebraic solution.

- **Option B:**
  - The intersection point \(\left(\frac{5}{4}, \frac{15}{4}\right)\) does not match our algebraic solution.

- **Option C:**
  - The intersection point (-6, 11) does not match our algebraic solution.

### Conclusion:
Option A, which shows the intersection point at (3, 2), is the correct answer.

Would you like more details or have any questions about this?

Here are some related questions you might find useful:

1. How can you graphically verify the solution to a system of linear equations?
2. What are some common methods to solve systems of linear equations?
3. How does changing the coefficients in a linear equation affect its graph?
4. What is the significance of the intersection point in a system of linear equations?
5. How do you determine the slope of a line from its equation?
6. How can you find the x- and y-intercepts of a linear equation?
7. What are the characteristics of parallel and perpendicular lines?
8. How can graphing software or tools help in solving linear equations?

**Tip:** When verifying solutions graphically, always ensure that the coordinates match both the x- and y-values accurately on the graph.

Learn how to graph and find the point of intersection for the linear equations x + y = 5 and y = 3x - 7. Detailed step-by-step solution provided, verifying algebraically and graphically. Suitable for students in Grades 7-9 studying linear equations and graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation