Final answer:
By establishing a linear equation based on the rent per square foot for the given office sizes, we find that the monthly rent for a 1500 square foot office is $1325.
Step-by-step explanation:
To solve for the monthly rent of a 1500 square foot office, we can establish a linear equation based on the given information about other office sizes and their respective rents. We're given two points: (800, $975) and (1100, $1125). Let's denote the size of the office in square feet as x and the monthly rent as y. We need to find the slope of the line, which is the change in rent per square foot. The slope m is calculated as:
m = (y2 - y1) / (x2 - x1)
Substituting in the values we have:
m = ($1125 - $975) / (1100 - 800) = $150 / 300 = $0.50 per sq ft
Now we can use the point-slope form to find the equation of the line:
y - y1 = m(x - x1)
Using one of the points, say (800, $975):
y - $975 = $0.50(x - 800)
Let's solve for y when x = 1500:
y - $975 = $0.50(1500 - 800)
y - $975 = $0.50 × 700
y - $975 = $350
y = $350 + $975
y = $1325
Therefore, the monthly rent for a 1500 square foot office is $1325.