Question

6. The graph shows how the value of a car changes over time.

Value (dollars)
30,000
25,000
20,000
15,000
10,000
5,000
Car
0 1 2 3 4 5 6 7 8 9 10
Time (years)
Which function best represents the relationship shown in the graph?
Oy=-3000x + 9
O y = 27000x + 9
O y = 27000x - 3000
O y = -3000x + 27000

help please

Answer 1

The graph shows a linear relationship where the value of the car decreases as time passes. We can see that after 0 years (when the car is brand new), its value is $30,000, and after 10 years, its value is $5,000.

We can use the slope-intercept form of a linear function (y = mx + b), where m is the slope and b is the y-intercept, to find the function that represents this relationship.

The slope is found by taking the difference in y-values (change in value) divided by the difference in x-values (change in time):

slope = (5000 - 30000) / (10 - 0) = -2500

The y-intercept is the value of the car when it is brand new, which is $30,000.

So, the equation of the line is:

y = -2500x + 30000

This matches the form of the equation y = -3000x + 27000, which is option (D), after we simplify it by combining the constants:

y = -3000x + 27000 = -2500x + 30000

Therefore, the function that best represents the relationship shown in the graph is y = -3000x + 27000.