Question

question 14 (1 point) listen the price of a car is $24,000 when it is new, but decreases in value by $1200 per year. create an algebraic expression that represents the value of the car after any number of years. enter your answer in the following form: b+m*x where b is the constant term and m is the coefficient, and x is the variable.

Explanation:

Step1: Define variables

Let \( x \) be the number of years, and \( V \) be the value of the car. The initial value (when \( x = 0 \)) is \( \$24000 \), and the rate of decrease is \( \$1200 \) per year. Since it's a decrease, the coefficient \( m \) will be negative.

Step2: Form the expression

The general form is \( b + m \times x \). Here, \( b = 24000 \) (initial value), \( m=- 1200 \) (rate of decrease), and \( x \) is the number of years. So the expression is \( 24000-1200x \) (which can be written as \( 24000+(- 1200)x \) to match the required form \( b + m\times x \)).

Answer:

\( 24000-1200x \) (or \( 24000+(-1200)x \))