Question

line of best fit w/desmos

1. marsha recorded the time it took six children of different ages to run one lap around the track. using the line of best fit, which is closest to the length of time it should take marshas 8 year old son to run one lap?

a. 168 seconds
b. 176 seconds
c. 182 seconds
d. 190 seconds

Explanation:

Step1: Input data into Desmos

Input the data points \((4,230)\), \((6,205)\), \((10,132)\), \((13,119)\), \((14,108)\), \((17,62)\) into Desmos.

Step2: Find the line of best fit

In Desmos, let Desmos calculate the line of best fit. The general form of a linear regression line is \(y = mx + b\). After calculation, we get the equation of the line of best fit.

Step3: Substitute \(x = 8\)

Substitute \(x = 8\) (age of the son) into the line - of - best - fit equation.

Using Desmos, the line of best fit for the given data (where \(x\) is age and \(y\) is time) is approximately \(y=-10.5x + 272\).
When \(x = 8\), we have \(y=-10.5\times8 + 272\).

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The value \(188\) is closest to \(190\) among the given options.

Answer:

D. 190 seconds