Answer
The line that represents the proportional relationship is [tex]y=0.5x[/tex]. 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 [tex]m=\frac{y}{x}[/tex]
where
[tex]m[/tex] is the slope of the line
[tex]y[/tex] is the total cost
[tex]x[/tex] is the number of cookies
We know that Timothy bought 10 cookies for $5.00, so [tex]x=10[/tex] and [tex]y=5[/tex]. Let's replace the values to find the slope of our line:
[tex]m=\frac{y}{x}[/tex]
[tex]m=\frac{5}{10}[/tex]
[tex]m=0.5[/tex]
Now that we have the slope of our line, we can find the equation for the total cost of [tex]x[/tex] cookies:
[tex]m=\frac{y}{x}[/tex]
[tex]0.5=\frac{y}{x}[/tex]
[tex]0.5x=y[/tex]
[tex]y=0.5x[/tex]
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 [tex]x[/tex] in our line equation. Let's say that the other point will be the total cost of 8 cookies, so [tex]x=8[/tex]
[tex]y=0.5x[/tex]
[tex]y=0.5(8)[/tex]
[tex]y=8[/tex]
Therefore, our second point is (8, 4)
Now we can join our point with our line as shown in the picture.
