Mary owns a small business. she spent $4,500 to get the business started. she has noticed that her monthly operating costs have been consistent. after five months, she has spent a total of $5,250 in start-up costs and monthly operating costs. in a linear model of this situation, which of the following statements applies? a. an additional month of business operation is associated with an additional $50 in costs. b. an additional month of business operation is associated with an additional $150 in costs. c. an additional month of business operation is associated with an additional $750 in costs. d. an additional month of business operation is associated with an additional $500 in costs.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer