Malachi took cans to the recycling plant and put them into the can-crusher one at a time. After he had already crushed some of the cans, he started recording the number of cans he crushed per minute. The table shows how many cans Malachi put in the can-crusher at different times. What is the equation that represents Malachi’s situation? (y – 65) = __ (x – __ ) is the answer (y – 65) = 8 (x – 13 ) ?
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differences in minutes: 2 2 2 (x differences) differences in cans crushed: 16 16 16 (y differences) Since the same differences in x causes same differences in y, this is a linear relationship. The slope of the straight line is: difference in y / difference in x = 16 / 2 = 8. The equation of the line in slope-point form is: y - y1 = m(x - x1) m = 8. If we choose (5,65) as the point from the table then: y - 65 = 8(x - 5)
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