Question

Tony has 6 dollars in change in his car. Every time he drives to visit his grandma, he pays $1.25 in tolls. Which graph represents the change Tony has in his car?

Answer 1

The required function is
`y=6-1.25x`. The graph of this function is shown below.

Explanation:

It is given that Tony has 6 dollars in change in his car. Every time he drives to visit his grandma, he pays $1.25 in tolls.

Let Tony visit his grandma be x.

The remaining change Tony has in his car is defined by the function

`y=6-1.25x`

It is a decreasing function. The value of y can not be negative.

`0=6-1.25x`

`x=4.8`

The graph is defined from x=0 to x=4.8.

Therefore the required function is
`y=6-1.25x`. The graph of this function is shown below.

Answer 2

Let
`x` be the number of times Tony drives to visit his grandma, and let
`y` represent the amount of change Tony has in his car.

Since he pays $1.25 in tolls every time he visit his grandma, the amount of change in his car is going to decrease by $1.25 every visit. We know form our problem that he initially has 6 dollars in change in his car. Since
`y` represents the amount of change and
`x` the number of visits, we can relate all the variables and quantities using a linear equation:

`y=6-1.25x`

To graph our linear equation, we just need to find two points and join them with a line.

The easiest points we can find are the
`y` and
`x`-intercepts.

- To find the
`y-intercept` we just need to replace
`x` with zero and solve for
`y`:

`y=6-1.25x`

`y=6-1.25(0)`

`y=6`

So, our first point is (0,6)

- To find the
`x-intercept` we just need to replace
`y` with zero and solve for
`x`:

`0=6-1.25x`

`-6=-1.25x`

`x=(-6)/(-1.25)`

`x=4.8`

Our second point is (4.8,0)

Now we can join those two points with a line.

we can conclude that the graph that represents the change Tony has in his car is the one in the picture: