9. The square footage and monthly rental of 15 similar one-bedroom apartments yield the linear regression formula [tex]y = 1.3485x + 840.51[/tex], where [tex]x[/tex] represents the square footage and [tex]y[/tex] represents the monthly rental price. Round answers to the nearest whole number.

a. Determine the monthly rent for an apartment with 1,200 square feet.

b. Determine the square footage of an apartment with a monthly rent of [tex]\$1,900[/tex].

Sure! Let's solve this problem step-by-step.

We are given a linear regression formula for determining the monthly rental price, [tex]$ y = 1.3485x + 840.51 $[/tex], where [tex]$ x $[/tex] is the square footage of the apartment.

### Part (a)

We need to find the monthly rent for an apartment with 1,200 square feet.

1. Substitute the square footage into the formula:
[tex]\[
y = 1.3485 \times 1200 + 840.51
\][/tex]

2. Calculate:
[tex]\[
y = 1618.2 + 840.51 = 2458.71
\][/tex]

3. Round the result to the nearest whole number:
[tex]\[
y \approx 2459
\][/tex]

So, the monthly rent for an apartment with 1,200 square feet is approximately [tex]$\$2459$[/tex].

### Part (b)

We need to find the square footage of an apartment with a monthly rent of [tex]$\$1,900$[/tex].

1. Set the equation for [tex]$ y $[/tex] to 1900 and solve for [tex]$ x $[/tex]:
[tex]\[
1900 = 1.3485x + 840.51
\][/tex]

2. Subtract 840.51 from both sides:
[tex]\[
1059.49 = 1.3485x
\][/tex]

3. Divide by 1.3485 to solve for [tex]$ x $[/tex]:
[tex]\[
x = \frac{1059.49}{1.3485} \approx 785.8
\][/tex]

4. Round the result to the nearest whole number:
[tex]\[
x \approx 786
\][/tex]

So, the square footage of an apartment with a monthly rent of [tex]$\$1,900$[/tex] is approximately 786 square feet.