Answer :
Final answer:
The equation for the rent based on square footage is R = ($4/3)S - $50. Using this formula, the predicted rent for 1200 square feet of space at West Main Street Office Rentals is $1550.
Explanation:
To find the equation for the rent based on the square footage, we need to first determine the slope of the line that represents the relationship between rent and space. Using the two points provided (600 sq ft, $750) and (900 sq ft, $1150), we calculate the slope (m) as:
m = (change in rent) / (change in square footage) = ($1150 - $750) / (900 sq ft - 600 sq ft) = $400 / 300 sq ft = $4/3 per sq ft.
Once we have the slope, we can use one of the points to find the y-intercept (b) of the equation. Using the point (600 sq ft, $750), the equation in slope-intercept form (y = mx + b) is:
750 = ($4/3) *600 + b
b = 750 - ($4/3) *600
b = 750 - 800
b = -$50
Now, the slope-intercept form of the equation representing the rent (R) in dollars for a given space (S) in square feet is:
R = ($4/3)S - $50
To predict the rent for 1200 square feet of space:
R = ($4/3) * 1200 - $50
R = $1600 - $50
R = $1550
Therefore, the predicted rent for 1200 square feet of space is $1550.