Question

The graph shows the relationship between pounds of grapes, g, and their cost, c.

Use the graph to complete the statements.
a) For every dollar you spend, you can get _________
pounds of grapes.
b) For each pound of grapes, you would need $__________

Answer 1

For every dollar you spend, you can get half a pound of grapes.
For every pound of grapes, you would need two dollars.

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Answer 2

Step 1

Let

x------> the cost in dollar

y-----> the pounds of grapes

`A(0,0)\ B(2,1)`

we know that

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

The line in the graph represent a direct variation

Find the constant of proportionality k

`y/x=k`------> substitute point B ----->
`1/2=k`

The slope is equal to the constant of proportionality

so

`m=0.50\ (pounds)/(\$)`

the linear equation is
`g=0.50c`

therefore

the answer Part a) is

For every dollar you spend, you can get
`0.50` pounds

Step 2

Find the cost for one pound of grapes

Let

`g=1\ pound`

substitute the value of g in the linear equation and solve for c

`g=0.50c`

`1=0.50c`

`c=1/0.50=2\$`

therefore

the answer Part b) is

For each pound of grapes, you would need
`2\$`