Question

Timothy bought 10 cookies for $5.00. Let x represent the number of cookies purchased, and let y represent the total cost. Graph the line that represents the proportional relationship.

Answer 1

The line that represents the proportional relationship is
`y=0.5x`. Check the graph in the picture.

Explanation

We know that x represent the number of cookies purchased and y represent the total cost, so the unit cost of the cookies, which is the slop of the line, will be given by
`m=(y)/(x)`

where

`m` is the slope of the line

`y` is the total cost

`x` is the number of cookies

We know that Timothy bought 10 cookies for $5.00, so
`x=10` and
`y=5`. Let's replace the values to find the slope of our line:

`m=(y)/(x)`

`m=(5)/(10)`

`m=0.5`

Now that we have the slope of our line, we can find the equation for the total cost of
`x` cookies:

`m=(y)/(x)`

`0.5=(y)/(x)`

`0.5x=y`

`y=0.5x`

Finally, to graph our line, we just need to plot tow points. We already know that Timothy bought 10 cookies for $5.00, so one point is (10, 5)

To find another point we can plug any number between 1 and 10 (the possible number of cookies Timothy can buy) for
`x` in our line equation. Let's say that the other point will be the total cost of 8 cookies, so
`x=8`

`y=0.5x`

`y=0.5(8)`

`y=8`

Therefore, our second point is (8, 4)

Now we can join our point with our line as shown in the picture.