The rent charged for space in an office building is a linear relationship related to the size of the space rented. At West Main Street Office Rentals, $750 is charged for 600 square feet of space, and $1150 is charged for 900 square feet of space.

Write an equation in slope-intercept form for the rent at West Main Street Office Rentals and use it to predict the rent for 1200 square feet of space.

The slope-intercept form of the equation for the rent at West Main Street Office Rentals is y = (4/3)x - 50. Using this equation, we predict that the rent for 1200 square feet of space will be $1550.

Explanation:

To find the equation in slope-intercept form that represents the relation between the size of an office space and the rent charged at West Main Street Office Rentals, we need to find the slope (m) and the y-intercept (b) using the given points (600, 750) and (900, 1150).

The slope (m) is calculated by taking the difference in rent and dividing it by the difference in square footage:

m = (1150 - 750) / (900 - 600) = 400 / 300 = 4/3 or approximately 1.33

Thus, for every additional square foot of office space, the rent increases by $1.33. Next, we use one of the points to solve for the y-intercept (b). We can use the point (600, 750):

750 = (4/3)(600) + b

750 = 800 + b

b = 750 - 800

b = -50

So the equation in slope-intercept form is:

y = (4/3)x - 50

To predict the rent for 1200 square feet of space, we substitute x with 1200 in the equation:

y = (4/3)(1200) - 50

y = 1600 - 50

y = 1550

The predicted rent for 1200 square feet of space is $1550.