bought a new car in 2011 for 25000. in 2015, joe was offered a fair price of 12000 for his car but he turned it down. build a linear algebraic model, that helps joe find the car's value when it is t years old

Accepted Solution

Answer:[tex]y=-3,250t+25,000[/tex]Step-by-step explanation:we know thatThe linear equation in slope intercept form is equal to[tex]y=mx+b[/tex]wherem is the slope of unit rate of the linear equationb is the y-intercept or initial value of the linear equationLett ----> the number of years since 2011y --->the car's valueIn this problem the year 2011 represent t=0sothe year 2015, represent t=4 years (2015-2011)we have the ordered pairs(0,25,000) ----> represent the y-intercept(4,12,000)Find the slope mThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{t2-t1}[/tex] substitute the values[tex]m=\frac{12,000-25,000}{4-0}[/tex] [tex]m=\frac{-13,000}{4}[/tex] [tex]m=-\$3,250\ per\ year[/tex] ---> is negative because is a decreasing functionwe have[tex]b=\$25,000[/tex] ----> value of y when the value of x is equal to zero (initial value)substitute the given values[tex]y=-3,250t+25,000[/tex]