Question

A friend gave Ms. Morris a gift card for a local car wash. The table shows the linear relationship of how the value left on the card relates to the number of car washes.

A.write an equation that shows the number of dollars left on the card.

B. Explain the meaning of the negative slope in this situation.

C. What is the maximum value of X that makes sense in this context? Explain.

Answer 1

A. y=-1.5x+30
B. it's negative because he is using money on the card
C.20, because that is the maximum amount of washes you can get for 30

Answer 2

x = 20, that is, after washing 20 cars.

Explanation:

To write the equation that model this problem we have to use slope-intercept formula:
`y=mx+b`.

The slope can be found using its definition, and two points from the table, could be
`(0;30)` and
`(12;12)`:

`m=(12-30)/(12-0)=-(-18)/(12)=-(6)/(4)=-(3)/(2)`

From the table, we observe the intercept point
`(0;30)`, which is the interception with y-axis, this is the meaning of
`b`. So, replacing all values in the slope-intercept formula, we have:

`y=-(3)/(2)x+30`

The meaning of the negative slope means that the functions is decreasing, that is, the amount of money decreases, while the number of car washed increase, that is a decreasing relationship.

In addition, the minimum value for x that make sense is when y = 0, that is, when the card has no money left, which is:

`0=-(3)/(2)x+30\\-30=-(3)/(2)x\\x=(60)/(3)=20`

Therefore, the maximum value for x that makes sense to the problem is x = 20, that is, after washing 20 cars.