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)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
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Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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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.
Transcribed Image Text: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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