Question

[Table] A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below. Linear or Quadratic? Equation: Approximate cost of home 90 miles from NYC?

Linear equations and graphs
ANSWERED
asked 2021-02-09
[Table]
A real-estate agent is trying to determine the relationship between the distance a 3-bedroom home is from New York City and its average selling price. He records the data for 6 homes shown below.
Linear or Quadratic?
Equation:
Approximate cost of home 90 miles from NYC?

Answers (1)

2021-02-10

Input the x-values under L1 in a graphing calculator and the yy-values, in thousands, under L2 (for example, input 755,000 as 755). Then graph the scatterplot to determine if it's linear or quadratic:

The points approximately lie on a straight line so the data is linear.
Use the LinReg feature on your graphing calculator to find the values of aa and bb for the line of best fit:

Since \(a \approx −4.3\) and \(b \approx 795.6\), the equation is \(y=−4.3x+795.6.\)
If a home is \(x=90\) miles from NYC, then \(y=−4.3(90)+795.6=408.6 \approx 409\) (round to the nearest whole number since the costs in the table are rounded to the nearest thousand). The cost of the home is then about $409,000

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