**Problem Statement:**A house was purchased for $66,000. After 5 years, the value of the house was $101,000. Find a linear equation that models the value of the house after $ x $ years.**Explanation:**To solve this problem, we need to determine the linear equation that represents the house's value $ V(x) $ over time, where $ x $ represents the number of years that have passed since the house was purchased.**Step-by-Step Solution:**1. **Identify Initial Value and Final Value:** - Initial value when $ x = 0 $: $66,000 - Final value when $ x = 5 $: $101,0002. **Determine the Rate of Change (Slope):** The slope ($ m $) of the linear equation can be calculated using the formula: \[ m = \frac{{V(5) - V(0)}}{5 - 0} \] In this case: \[ m = \frac{101,000 - 66,000}{5} = \frac{35,000}{5} = 7,000 \] So, the rate of change is $7,000 per year.3. **Construct the Linear Equation:** The general form of a linear equation is: \[ V(x) = mx + b \] Where: - $ m $ is the slope - $ b $ is the initial value when $ x = 0 $ Using the values we found: \[ V(x) = 7,000x + 66,000 \]Therefore, the linear equation that models the value of the house after $ x $ years is:\[V(x) = 7,000x + 66,000\]

Here we have to find the linear equation

Answered: A house was purchased for $66,000.…

A house was purchased for $66,000. After 5 years the value of the house was $101,000. Find a linear equation that models the value of the house after x years.

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

**Problem Statement:**

A house was purchased for $66,000. After 5 years, the value of the house was $101,000. Find a linear equation that models the value of the house after $ x $ years.

**Explanation:**

To solve this problem, we need to determine the linear equation that represents the house's value $ V(x) $ over time, where $ x $ represents the number of years that have passed since the house was purchased.

**Step-by-Step Solution:**

1. **Identify Initial Value and Final Value:**
- Initial value when $ x = 0 $: $66,000
- Final value when $ x = 5 $: $101,000

2. **Determine the Rate of Change (Slope):**
The slope ($ m $) of the linear equation can be calculated using the formula:
\[
m = \frac{{V(5) - V(0)}}{5 - 0}
\]
In this case:
\[
m = \frac{101,000 - 66,000}{5} = \frac{35,000}{5} = 7,000
\]
So, the rate of change is $7,000 per year.

3. **Construct the Linear Equation:**
The general form of a linear equation is:
\[
V(x) = mx + b
\]
Where:
- $ m $ is the slope
- $ b $ is the initial value when $ x = 0 $

Using the values we found:
\[
V(x) = 7,000x + 66,000
\]

Therefore, the linear equation that models the value of the house after $ x $ years is:
\[
V(x) = 7,000x + 66,000
\]

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