Question

question 2 of 25
the resale value of a certain car decreases over time. use the line of best fit
to estimate what the car will be worth in 7 years.

text description for graph

a. $5500
b. $2257
c. $9000
d. $3500

Explanation:

Step1: Find the slope of the line of best fit

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using the points \((2,8)\) and \((8,5)\) (where \(x\) is time in years and \(y\) is resale value in thousands of dollars), \(m=\frac{5 - 8}{8 - 2}=\frac{-3}{6}=-\frac{1}{2}\)

Step2: Use the point - slope form \(y - y_1=m(x - x_1)\)

Using the point \((2,8)\) and \(m =-\frac{1}{2}\), \(y - 8=-\frac{1}{2}(x - 2)\). Simplify: \(y-8=-\frac{1}{2}x + 1\), then \(y=-\frac{1}{2}x+9\)

Step3: Substitute \(x = 7\) into the equation

\(y=-\frac{1}{2}(7)+9=-\frac{7}{2}+9=\frac{-7 + 18}{2}=\frac{11}{2}=5.5\) (since \(y\) is in thousands of dollars)

Answer:

A. \(\$5500\)