Questions: 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. 0.31 / lb. 1.60 / lb. 5.64 / lb. 0.18 / lb.

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. 0.31 / lb. 1.60 / lb. 5.64 / lb. 0.18 / lb.
Transcript text: 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. \$0.31 / lb. $\$ 1.60$ / lb. $\$ 5.64$ / lb. \$0.18 / lb.
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Solution

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Solution Steps

Step 1: Calculate the change in weight

To find the slope, we first calculate the change in weight, \(\Delta x\), which is \(x_2 - x_1 = 30 - 3.5 = 26.5\).

Step 2: Calculate the change in cost

Next, we calculate the change in cost, \(\Delta y\), which is \(y_2 - y_1 = 9.2 - 4.5 = 4.700\).

Step 3: Calculate the slope

The slope, \(m\), is the ratio of the change in cost to the change in weight, \(m = \frac{\Delta y}{\Delta x} = \frac{4.700}{26.5} = 0.177\).

Step 4: Round the calculated slope

Finally, we round the calculated slope to the nearest 2 decimal places, resulting in \(m = 0.18\).

Final Answer:

The slope of the line connecting the two data points is \(m = 0.18\).

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