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This scatter plot shows the relationship between the age of a refrigerator and the amount of electricity the refrigerator uses each day. Based on the line of best fit of the data, which is the best prediction of the amount of electricity used each day by a refrigerator that is 4 years old? 1.75kwh/day ) B. 2.25kwh/day C. 2.5kwh/day D. 3.0kwh/day

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This scatter plot shows the relationship between the age of a refrigerator and the amount of electricity the refrigerator uses each day. Based on the line of best fit of the data, which is the best prediction of the amount of electricity used each day by a refrigerator that is 4 years old? 1.75kwh/day ) B. 2.25kwh/day C. 2.5kwh/day D. 3.0kwh/day

This scatter plot shows the relationship between the age of a refrigerator and the amount of electricity the refrigerator uses each day. Based on the line of best fit of the data, which is the best prediction of the amount of electricity used each day by a refrigerator that is 4 years old? 1.75kwh/day ) B. 2.25kwh/day C. 2.5kwh/day D. 3.0kwh/day

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VesperMaster · Tutor for 5 years

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To predict the amount of electricity used each day by a refrigerator that is 4 years old using the line of best fit, we need to follow these steps:Step 1: Determine the slope of the line of best fit.The slope (m) of a line can be calculated using two points on the line with the formula:\[m = \frac{\Delta y}{\Delta x}\]where \(\Delta y\) is the change in the y-values and \(\Delta x\) is the change in the x-values of the two points.From the picture details, we have two points on the line: (0, 0) and (6, 2.8).Step 2: Calculate the slope using the given points.\[m = \frac{2.8 - 0}{6 - 0} = \frac{2.8}{6} = \frac{14}{30} = \frac{7}{15}\]Step 3: Use the slope to find the y-value (electricity consumption) when x (age of the refrigerator) is 4.We can use the point-slope form of the equation for a line, which is:\[y - y_1 = m(x - x_1)\]where \((x_1, y_1)\) is a point on the line (we can use the point (0, 0) since it's given) and m is the slope.Step 4: Plug in the values and solve for y when x is 4.\[y - 0 = \frac{7}{15}(4 - 0)\]\[y = \frac{7}{15} \times 4\]\[y = \frac{28}{15}\]\[y = 1.866\overline{6}\]Step 5: Round to the nearest option provided.The value of \(1.866\overline{6}\) kWh/day is closest to option A, which is \(1.75\) kWh/day.Answer:A. \(1.75 \mathrm{kwh} / \mathrm{day}\)
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