For the relation y=5x-5, sketch the graph of the relation and its inverse, then write the equation for the inverse. The problem presents the relation $ y = 5x - 5 $. You are required to sketch the graph of this relation and its inverse, then write the equation for the inverse. ### Graph Description:- The graph is a coordinate plane with both horizontal (x-axis) and vertical (y-axis) scales ranging from -7 to 7.- The axes are marked by grid lines, creating a detailed grid for plotting.### Steps to Solve:1. **Sketch the Graph of the Relation:** - Use the equation $ y = 5x - 5 $. - Find points to plot: You can use values of $ x $ to find corresponding $ y $ values. For example, if $ x = 0 $, then $ y = -5 $. When $ x = 1 $, $ y = 0 $; when $ x = 2 $, $ y = 5 $, etc. - Plot these points on the graph and draw a straight line through them.2. **Determine the Inverse:** - Swap $ x $ and $ y $ in the equation: $ x = 5y - 5 $. - Solve for $ y $ to find the inverse equation: \[ x + 5 = 5y \quad \Rightarrow \quad y = \frac{x + 5}{5} \] - This equation represents the inverse relation.3. **Sketch the Graph of the Inverse:** - Use the inverse equation $ y = \frac{x + 5}{5} $. - Find points to plot: When $ x = 0 $, $ y = 1 $; for $ x = 5 $, $ y = 2 $, etc. - Plot these points and draw a straight line through them on the same graph.### Conclusion:This activity would involve sketching both the original and inverse relations on the coordinate plane to help visualize the relationship and understand how finding inverses works algebraically and graphically.

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Answered: For the relation: y = 5x - 5, sketch…

For the relation: y = 5x - 5, sketch the graph of the relation and its inverse, then write the equation for the Ihverse. 6- 5- 4+ 3+ 2+ -7 -6 -5 4 -3 -2 -1 4 6. 7. -3+ 4+ -5- -6 7+ 2.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

For the relation y=5x-5, sketch the graph of the relation and its inverse, then write the equation for the inverse.

The problem presents the relation $ y = 5x - 5 $. You are required to sketch the graph of this relation and its inverse, then write the equation for the inverse.

### Graph Description:
- The graph is a coordinate plane with both horizontal (x-axis) and vertical (y-axis) scales ranging from -7 to 7.
- The axes are marked by grid lines, creating a detailed grid for plotting.

### Steps to Solve:
1. **Sketch the Graph of the Relation:**
- Use the equation $ y = 5x - 5 $.
- Find points to plot: You can use values of $ x $ to find corresponding $ y $ values. For example, if $ x = 0 $, then $ y = -5 $. When $ x = 1 $, $ y = 0 $; when $ x = 2 $, $ y = 5 $, etc.
- Plot these points on the graph and draw a straight line through them.

2. **Determine the Inverse:**
- Swap $ x $ and $ y $ in the equation: $ x = 5y - 5 $.
- Solve for $ y $ to find the inverse equation:
\[
x + 5 = 5y \quad \Rightarrow \quad y = \frac{x + 5}{5}
\]
- This equation represents the inverse relation.

3. **Sketch the Graph of the Inverse:**
- Use the inverse equation $ y = \frac{x + 5}{5} $.
- Find points to plot: When $ x = 0 $, $ y = 1 $; for $ x = 5 $, $ y = 2 $, etc.
- Plot these points and draw a straight line through them on the same graph.

### Conclusion:
This activity would involve sketching both the original and inverse relations on the coordinate plane to help visualize the relationship and understand how finding inverses works algebraically and graphically.

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