# [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
[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.
Equation:
Approximate cost of home 90 miles from NYC?

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