Question

4.3 test (cs): data and mathematical modeling
he resale value of a certain car decreases over time. use the line of best
estimate what the car will be worth in 7 years.
a. $3500
b. $2257
c. $5500
d. $9000

Explanation:

Step1: Find the slope of the line

Use the formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\) with points \((2,8)\) and \((8,5)\).
\(m=\frac{5 - 8}{8 - 2}=\frac{-3}{6}=-\frac{1}{2}\)

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

Using the point \((2,8)\) and \(m =-\frac{1}{2}\), we have \(y - 8=-\frac{1}{2}(x - 2)\)
\(y-8=-\frac{1}{2}x + 1\)
\(y=-\frac{1}{2}x+9\)

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

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

Answer:

C. \(\$5500\)