Consider V as the value of the car and t as the number of years.
V=- 4000t+30 000
Practice makes perfect
We are told that the value of a new car decreases 4000 dollars per year. The amount decreased can be written as the product of 4000 multiplied by the number of years t.
Amount Decreased= 4000t
To find the initial price of the car, consider that after three years the car worth 18 000 dollars. Then, the initial price of the car will be equal to the sum of the amount decreased in three years and 18 000 dollars.
Initial Price= 4000(3) +18 000Let's calculate this value!
We want to draw a graph that shows the value of the car after t years by considering V as the value of the car. To do so, consider that the point (0,30 000) represents the initial price and the point (3,18 000) as the value of the car after 3 years. Let's plot these points in a coordinate plane and draw a line that passes through them!
This line represent the value of the car after t years. Now, we can write the equation for this line by recalling the slope-intercept form.
y= mx+ b
In this form, m is the slope and b is the y-intercept. In our case, y will represents the value of the car V and x will be the years t.
V= mt+ b
Notice that the initial price of the car is always equal to 30 000. Then if we consider that V represents the value of the price that we have after t years, the y-intercept of our equation will be 30 000. The slope will be the amount of money that the car decreases per yer, which means that m= - 4000.
V= - 4000x+ 30 000
