Question

4 Raquel earned S105 for baking seven pies one week. The following week she earned$60 for baking four pies. On the third week, she did not bake any pies or earnany moneyPart AUse the graph below to show the relationship between the number of pies Raquelbaked and the amount of money she earned each week. Plot the three data pointsfrom the problem statement and draw a line connecting the points.34 5Ples BakedPart BIs there a proportional relationship between the number of pies Raquel bakes andthe money she earns? Use the graph to explain your answer.

Answer 1

We are given a relationship between pies and earnings, we are asked wheater the relationship is linear. Let "x" be the number of pies and "y" its cost. Then, according to the statements of the problem we have the following points.

It says that she earned 105 for 7 pies, this means the point:

`(x,y)=(7,105)`

It also says that she earned 60 for 4 pies, which means the point:

`(x,y)=(4,60)`

It also says that she earned 0 for baking 0 pies, that is the point:

`(x,y)=(0,0)`

Since the point passes through the point (0,0) the form of its equation is the following:

`y=mx`

To find the value of "m" we replace one of the given points. Let's pick (4,60), this means that when x = 4, y = 60.

`60=m(4)`

Solving for "m"

`m=15`

Replacing in the equation:

`y=15x`

Now, the relationship is proportional if the given point (7,105) is part of the line. To see that we replace x = 7 and we should get y = 105.

`\begin{gathered} y=15(7) \\ y=105 \end{gathered}`

Since we got y = 105, the relationship is proportional.

The graph of the points looks like this: