Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN: 9780134463216
Author: Robert F. Blitzer
Publisher: PEARSON
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**Graphing a Linear Equation: Gym Membership**

**Problem Statement:**

Make a graph of the situation. The equation \( y = 15x + 20 \) represents the cost \( y \) (in dollars) of a gym membership after \( x \) months.

**Blank Graph:**

A grid is provided with the following features:
- The x-axis is labeled "Gym membership (months)" and is marked from 0 to 10.
- The y-axis is labeled "Cost (dollars)" and is marked from -80 to 80.
- The graph is currently empty and is intended for plotting the linear relationship given by the equation.

**Equation:**

The given linear equation is \( y = 15x + 20 \).

**Solution Steps:**

1. **Equation Understanding:**
   - The equation \( y = 15x + 20 \) signifies that the cost of the gym membership starts at $20 and increases by $15 for each month.

2. **Table of Values (Optional Scratch Work):**
   - A table is suggested with:
     - \( x \) representing months (0, 1, 2)
     - \( y \) representing the cost (20, 35, 50)

   Example Table:
   \[
   \begin{array}{|c|c|}
   \hline
   x (\text{months}) & y (\text{dollars}) \\
   \hline
   0 & 20 \\
   1 & 35 \\
   2 & 50 \\
   \hline
   \end{array}
   \]

3. **Graphing Instructions:**
   - Plot the points on the graph using the table values.
   - Connect the points to visualize the linear relationship.

**Context:**

This task helps students understand how to interpret and graph linear equations in real-world contexts, such as calculating cumulative costs over time.
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Transcribed Image Text:**Graphing a Linear Equation: Gym Membership** **Problem Statement:** Make a graph of the situation. The equation \( y = 15x + 20 \) represents the cost \( y \) (in dollars) of a gym membership after \( x \) months. **Blank Graph:** A grid is provided with the following features: - The x-axis is labeled "Gym membership (months)" and is marked from 0 to 10. - The y-axis is labeled "Cost (dollars)" and is marked from -80 to 80. - The graph is currently empty and is intended for plotting the linear relationship given by the equation. **Equation:** The given linear equation is \( y = 15x + 20 \). **Solution Steps:** 1. **Equation Understanding:** - The equation \( y = 15x + 20 \) signifies that the cost of the gym membership starts at $20 and increases by $15 for each month. 2. **Table of Values (Optional Scratch Work):** - A table is suggested with: - \( x \) representing months (0, 1, 2) - \( y \) representing the cost (20, 35, 50) Example Table: \[ \begin{array}{|c|c|} \hline x (\text{months}) & y (\text{dollars}) \\ \hline 0 & 20 \\ 1 & 35 \\ 2 & 50 \\ \hline \end{array} \] 3. **Graphing Instructions:** - Plot the points on the graph using the table values. - Connect the points to visualize the linear relationship. **Context:** This task helps students understand how to interpret and graph linear equations in real-world contexts, such as calculating cumulative costs over time.
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