Critique Reasoning Sam drew a trend line that had about the same number of data points above it as below it, but did not pass through any data points. He then picked two data points to write the equation for the line. Is this a correct way to write the equation? Explain.
Marlene wanted to find a relationship between the areas and populations of counties in Texas. She plotted x (area in square miles) and y (population) for two counties on a scatter plot:
Kent County (903, 808) Edwards County (2118, 2002)
She concluded that the population of Texas counties is approximately equal to their area in square miles and drew a trend line through her points.
a. Critique Reasoning Do you agree with Marlene’s method of creating a scatter plot and a trend line? Explain why or why not.
b. Counterexamples Harris County has an area of 1778 square miles and a population of about 4.3 million people. Dallas County has an area of 908 square miles and a population of about 2.5 million people. What does this data show about Marlene’s conjecture that the population of Texas counties is approximately equal to their area?
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