The graph shows the relationship between the number of years after a car is purchased
and the car's value
Which statement correctly describes the relationship shown in the graph?
A)
The car's initial value is $18,000, and the car's value increases $2,000 each year.
B)
The car's initial value is $18,000, and the car's value increases $6,000 each year
C)
The car's initial value is $30,000, and the car's value decreases $2,000 each year.
D)
The car's initial value is $30,000, and the car's value decreases $6,000 each year

Answer:

C. The car's initial value is $30,000, and the car's value decreases $2,000 each year.

Step-by-step explanation:

first I looked at the graph and saw that the y-intercept(car's initial value) was 30,000 which allowed me to eliminate A and B. Then found the slope by using the [tex]\frac{y_{2} -y_{1} }{x_{2} -x_{1} }[/tex]= slope formula. [tex]\frac{24,000-30,000}{3-0}=\frac{-6,000}{3}=-2,000[/tex]. This tells us that the slope is -2,000 which means that the value decreases by 2,000 each month. So the correct answer is C.

The car's initial value is $30,000, and the car's value decreases by $2,000 each year. the correct answer would be an option (C).

The slope of a line is defined as the gradient of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The given graph shows the relationship between the number of years after a car is purchased and the car's value.

As per the graph, we take two points (0, 30,000) and (6, 18,000)

Here slope of the given graph is equal to the car's value decreases by each year.

So slope = (18,000 - 30,000)/(6-0) = -12,000/6 = -2000

This means the car's value decreases by $2,000 each year.

Thus, the car's initial value is $30,000, and the car's value decreases by $2,000 each year.

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