Answer :
Final answer:
The equation in slope-intercept form representing the relationship between size of office space rented and rental charge at West Main Street Office Rentals is y = 4/3x - 50, where y represents the rental charge and x represents the size of the office space.
Explanation:
To form an equation in slope-intercept form (y=mx+b), we have to find the slope (m) and y-intercept (b). The slope of the line is the change in y (the dependent variable, rent) divided by change in x (the independent variable, space rented). If we define rent as y and the size of the space as x, we can consider the two points given: (600, 750) and (900, 1150).
Step 1: Calculate the slope (m). The formula for slope is m = (y2 - y1) / (x2 - x1), so m = (1150 - 750) / (900 - 600) = 400 / 300 = 4/3. This indicates that each additional square foot of space rented increases the rent by 4/3 dollars.
Step 2: To find the y-intercept (b), we can use one of the points and solve for b in the equation y = mx + b. Substitute 750 for y, 600 for x and slope 4/3 for m in the equation, to get 750 = 4/3 * 600 + b, and solve for b. This gives b = -50.
Therefore, the equation for the rent at West Main Street Office Rentals is y = 4/3x - 50. Hence, this equation represents the relationship between the size of the office space rented and the amount of rent charged.
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