The rent charge for space in a stall is a linear relationship related to the size of the space rented. At Robinson’s Place stall rentals, Php 1,500 is charged for 7 square feet of space and Php 2,100 is charged for 10 square feet of space.

Write an equation in slope-intercept form for the rent at Robinson’s Place stall rentals.

A. \( R = 150x + 300 \)

B. \( R = 200x + 150 \)

C. \( R = 300x + 150 \)

D. \( R = 150x + 200 \)

To write the equation in slope-intercept form for the rent at Robinson’s Place stall rentals, we need to find the slope and the y-intercept. We are given two data points: (7, 1500) and (10, 2100). Using these points, we can calculate the slope using the formula: slope (m) = (change in y)/(change in x). The change in y is 2100 - 1500 = 600, and the change in x is 10 - 7 = 3. Therefore, the slope is 600/3 = 200.

Next, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept. Since we already know the slope (m = 200), we just need to find the y-intercept. We can substitute the values from one of the data points into the equation and solve for b. Using the point (7, 1500), we have: 1500 = 200(7) + b. Solving for b, we get b = 1500 - 1400 = 100. Therefore, the equation in slope-intercept form for the rent at Robinson’s Place stall rentals is: R = 200x + 100. Therefore, the correct answer is option B: R = 200x + 150.

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