1 answer:
Answer:
Step-by-step explanation:
The given problem is a subtraction problem between fractions. The first step in a problem like this is to convert both fractions to a common denominator. In other words, multiply both the numerator and denominator of a fraction by the same value such that the denominator of one of the fractions is the same as the other fraction. The numerator of a fraction is the value over the fraction bar, whereas the denominator is the value under it. Multiplying any fraction by a number over itself is the same as multiplying it by one, thus, the equation will remain true, and be equivalent to the original expression.
Convert to a common denominator,
Now perform the subtraction, subtract one numerator from the other, remember, do no perfrom any more operations with the denominators,
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Answer:
Step-by-step explanation:
If the car is depreciating at a constant rate, this indicates that the function is linear. We can find the equation for the linear function by first finding the slope of the line. Let's do that using the slope formula. The coordinates we will use to do this are found in (year, value). Our coordinates are (0, 21500) and (3, 14120). The first coordinate says that before any time goes by at all, meaning when the car was brand new, its value was 21500. The second coordinate says that after 3 years, the value of the car was 14120.
Filling in:
This is the slope. In the context of our problem, it means that for each year that goes by, the car's value goes down $2460.
Now we can use that slope and one of our coordinates to write the equation of the line. We can choose either one of the coordinates to write our equation. Let's use the first one, since it will be easier. Rest assured that regardless of which one you choose, you will get the same equation. We fill in the slope-inteercept form of a line, y = mx + b, where y is the y value from the coordinate, m is the slope we solved for, x is the x value from the same coordinate, and b is the y-intercept. We are solving for b.
21500 = -2460(0) + b and
21500 = 0 + b so
b = 21500. Our equation, then, is
y = -2460x + 21500
If we want to find the value of the car, y, in 5 years, x, we plug in 5 for x and solve for y.
y = -2460(5) + 21500 and
y = -12300 + 21500 so
y = $9200
That means that in 5 year the car will be worth only $9200 when it is 5 years old.