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Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs $4.50 per week to feed, while a Beagle weighs 30 pounds and costs $9.20 per week to feed.Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth.$1.60 / lb.$0.31 / lb.$0.18 / lb.$5.64 / lb.

Question

Jesse takes two data points from the weight and feed cost data set to calculate a slope, or average rate of change. A rat weighs 3.5 pounds and costs 4.50perweektofeed,whileaBeagleweighs30poundsandcosts4.50 per week to feed, while a Beagle weighs 30 pounds and costs 9.20 per week to feed.Using weight as the explanatory variable, what is the slope of the line between these two points? Answer choices are rounded to the nearest hundredth.1.60/lb.1.60 / lb.0.31 / lb.0.18/lb.0.18 / lb.5.64 / lb.

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Solution

The slope of a line is calculated by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line.

In this case, we are given two points: (3.5, 4.5) and (30, 9.2), where the x-values represent the weight of the animals and the y-values represent the cost to feed them.

Substituting these values into the formula, we get:

(9.2 - 4.5) / (30 - 3.5) = 4.7 / 26.5 ≈ 0.18

So, the slope of the line between these two points is approximately 0.18perpound.Thismeansthatforeachadditionalpoundofweight,thecosttofeedtheanimalincreasesbyabout0.18 per pound. This means that for each additional pound of weight, the cost to feed the animal increases by about 0.18. Therefore, the correct answer is $0.18 / lb.

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