Question

a proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y) is graphed, and the ordered pair (5,4) is on the original graphed line. Part A. what is the price of 1 pound of potatoes? Part B. what does the ordered pair (10,8) on the graph represent

Answer 1

Given a proportional relationship between the number of pounds of potatoes (x) and the price in dollars (y), it is assumed that

`\begin{gathered} (y)/(x)\text{ = K ------ equation 1} \\ \text{where K is a proportionality constant} \end{gathered}`

Thus, for the ordered pair (5, 4),

`\begin{gathered} (5,4)\Rightarrow(x,y) \\ K\text{ = }(y)/(x)=(4)/(5) \\ \Rightarrow K=(4)/(5) \end{gathered}`

This implies that

`\begin{gathered} (y)/(x)=(4)/(5) \\ \Rightarrow y=(4)/(5)x\text{ ----- equation 2} \end{gathered}`

A) Price of 1 pound of potatoes

`\begin{gathered} x=1 \\ y=\text{ unknown} \\ \text{From equation 2,} \\ y=(4)/(5)x \\ y=(4)/(5)(1) \\ y=0.8 \end{gathered}`

Thus, the price of 1 pound of potatoes is 0.8 dollars

B) The ordered pair (10,8) represents that the cost of 10 pounds of potatoes is 8 dollars.