Question

Martin has a gift card to a coffee shop. Each day he buys the same coffee. This table shows the amount remaining in dollars on the gift card on different days. Time (days) 2 4 5 7 Amount remaining ($) $24.10 $18.20 $15.25 $9.35

Which equation represents this situation, where x is the time and y is the amount remaining?
A) y+15.25=−2.95(x+5)
B) y+24.10=2.95(x−2)
C) y−9.35=−2.95(x−7)
D) y−18.20=−2.95(x+4)

Answer 1

The answer is C. y – 9.35 = −2.95(x – 7).

Explanation:

Answer 2

`y-9.35=-2.95(x-7)`

Explanation:

Time (days) 2 4 5 7

Amount remaining ($) $24.10 $18.20 $15.25 $9.35

We are supposed to find equation represents this situation, where x is the time and y is the amount remaining

So, we will use point slope form :

Formula :
`y-y_1=m{x_2-x_1}(x-x_1)`

Where
`m = (y_2-y_1)/(x_2-x_1)`

`(x_1,y_1)=(2,24.10)`

`(x_2,y_2)=(4,18.20)`

`m = (18.20-24.110)/(4-2)`

`m =-2.95`

Now (x_1,y_1)=(7,9.35)

Formula :
`y-y_1=m(x-x_1)`

Substitute the values:

`y-9.35=-2.95(x-7)`

So, Option c is true

Hence equation represents this situation, where x is the time and y is the amount remaining is
`y-9.35=-2.95(x-7)`