Question

Sean wrote the equation 9.25 = 5m, where m is the cost per pound of pears, to show the relationship between the total cost and the number of pears he bought at Quick Mart.

What is the unit cost per pears? Write an equation.

Does this relationship represent a proportional relationship? Use a graph to prove it. Explain how the graph proves the situation is a proportional relationship.

Answer 1

see the explanation

Explanation:

The correct question is

Sean wrote the equation 9.25=5m, where m is the cost per pound, to show the relationships between the total cost, $9.25, and the number of pounds of pears, write an equation to show the cost y of x pounds of pears, and use the equation to complete the table. then use the information in your table to make a graph

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`k=(y)/(x)` or
`y=kx`

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

Let

y ----> the total cost

x ---> the number of pounds of pears

In this problem we have a proportional relationship between the variables x and y

we have

`9.25=5m`

where

m is the cost per pound of pears

That means

The value of m and the value of the constant k of proportionality is the same

Find the value of m

`9.25=5m\\m=\$1.85\ per\ pound`

The linear equation is equal to

`y=1.85x`

Construct the table

assume different values of x and determine the value of y

`For\ x=0 ----> y=1.85(0)=0`

`For\ x=1 ----> y=1.85(1)=1.85`

`For\ x=2 ----> y=1.85(2)=3.70`

`For\ x=3 ----> y=1.85(3)=5.55`

`For\ x=4 ----> y=1.85(4)=7.4`

`For\ x=5 ----> y=1.85(5)=9.25`

therefore

`\begin{array}{cc}x(\text{Number of pounds}) & y(\text{Cost in dollars})\\0 & 0\\1 & 1.85\\2 & 3.7\\3 & 5.55\\4 & 7.4\\5 & 9.25\end{array}`

using a graphing tool

The grahp in the attached figure