Write an equation of the line and interpret the slope.

Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.
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**Title: Understanding Linear Equations and Slope**

**Objective:** Write an equation of the line and interpret the slope using the provided graphs.

---

**1. Interest-Free Loan**

**Graph Description:**
- The graph is titled "Interest-Free Loan."
- The x-axis represents "Payments (months)" ranging from 0 to 30.
- The y-axis represents "Balance (dollars)" ranging from 0 to 2000.
- Two key data points are indicated: (10, 1300) and (20, 800).

**Interpretation:**
- The line on the graph shows a downward trend, indicating that as payments increase, the loan balance decreases.
- To find the equation of the line, identify the slope using the formula:
  \[
  \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{800 - 1300}{20 - 10} = \frac{-500}{10} = -50
  \]
- Equation of the line: \( y = mx + b \)
  - \( m = -50 \) (slope)
  - Use one point, e.g., (10, 1300), to find \( b \):
  \[
  1300 = -50(10) + b \implies b = 1800
  \]
- Final equation: \( y = -50x + 1800 \)
- **Slope Interpretation:** The slope of -50 indicates that for each month of payment, the balance decreases by $50.

---

**2. Canoe Rental**

**Graph Description:**
- The graph is titled "Canoe Rental."
- The x-axis represents "Time (hours)" ranging from 0 to 6.
- The y-axis represents "Total Cost (dollars)" ranging from 0 to 50.
- Two key data points are indicated: (5, 45) and (2, 30).

**Interpretation:**
- The line shows an upward trend, indicating that as time increases, the total cost increases.
- Calculate the slope:
  \[
  \text{slope} = \frac{45 - 30}{5 - 2} = \frac{15}{3} = 5
  \]
- Equation of the line: \( y = mx + b \)
  - \( m =
Transcribed Image Text:**Title: Understanding Linear Equations and Slope** **Objective:** Write an equation of the line and interpret the slope using the provided graphs. --- **1. Interest-Free Loan** **Graph Description:** - The graph is titled "Interest-Free Loan." - The x-axis represents "Payments (months)" ranging from 0 to 30. - The y-axis represents "Balance (dollars)" ranging from 0 to 2000. - Two key data points are indicated: (10, 1300) and (20, 800). **Interpretation:** - The line on the graph shows a downward trend, indicating that as payments increase, the loan balance decreases. - To find the equation of the line, identify the slope using the formula: \[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{800 - 1300}{20 - 10} = \frac{-500}{10} = -50 \] - Equation of the line: \( y = mx + b \) - \( m = -50 \) (slope) - Use one point, e.g., (10, 1300), to find \( b \): \[ 1300 = -50(10) + b \implies b = 1800 \] - Final equation: \( y = -50x + 1800 \) - **Slope Interpretation:** The slope of -50 indicates that for each month of payment, the balance decreases by $50. --- **2. Canoe Rental** **Graph Description:** - The graph is titled "Canoe Rental." - The x-axis represents "Time (hours)" ranging from 0 to 6. - The y-axis represents "Total Cost (dollars)" ranging from 0 to 50. - Two key data points are indicated: (5, 45) and (2, 30). **Interpretation:** - The line shows an upward trend, indicating that as time increases, the total cost increases. - Calculate the slope: \[ \text{slope} = \frac{45 - 30}{5 - 2} = \frac{15}{3} = 5 \] - Equation of the line: \( y = mx + b \) - \( m =
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