High School

The square footage and monthly rental of 10 similar two-bedroom apartments yield the linear regression equation [tex]y = 1.165x + 615.23[/tex], where [tex]x[/tex] represents the square footage of the apartment and [tex]y[/tex] represents the monthly rental price.

a. Use the equation to determine the monthly rent for an apartment that has 1,500 square feet.

b. Based on the recommendation that you should spend no more than [tex]28\%[/tex] of your monthly gross income on housing, can Jacob afford this rental if he makes [tex]\$8,000[/tex] each month? Explain.

Answer :

Sure, I'd be happy to help explain how to solve the problem step by step:

### Part a: Determine the Monthly Rent for a 1,500 Square Foot Apartment

1. Understand the Equation: The linear regression equation given is [tex]\( y = 1.165x + 615.23 \)[/tex], where [tex]\( x \)[/tex] represents the square footage, and [tex]\( y \)[/tex] represents the monthly rental price.

2. Plug in the Square Footage: You're asked to determine the rent for an apartment with 1,500 square feet. So you'll substitute [tex]\( x = 1500 \)[/tex] into the equation.

3. Calculate the Rent:
[tex]\[
y = 1.165 \times 1500 + 615.23
\][/tex]

4. Result: After performing the calculation, the monthly rent for an apartment that has 1,500 square feet is approximately [tex]$2,362.73.

### Part b: Determine if Jacob Can Afford the Rent

1. Calculate Affordable Rent Based on Income:
- Jacob has a monthly income of $[/tex]8,000.
- The recommendation is to spend no more than 28% of the monthly gross income on housing.
- Calculate 28% of Jacob's monthly income:
[tex]\[
\text{Maximum Affordable Rent} = 0.28 \times 8000
\][/tex]

2. Result: Jacob can afford to spend up to [tex]$2,240.00 on rent per month.

3. Compare the Rent:
- The calculated rent for the 1,500 square foot apartment is $[/tex]2,362.73.
- Compare this with the maximum affordable rent of [tex]$2,240.00.

4. Conclusion: Since $[/tex]2,362.73[tex]$ exceeds $[/tex]2,240.00$, this means Jacob cannot afford this rental based on the 28% guideline for spending on housing.

I hope this explanation helps you understand how to arrive at the answers for both parts of the question!