Question

Jolene is making a line graph showing that the cost of grain is proportional to the number of pounds purchased. Jolene will plot the number of pounds on the x-axis and the cost in dollars on the y-axis. The coordinates Jolene graphs are shown in the table.

Which coordinate represents the unit rate, in dollars per pound of grain, and why?

Pounds Cost (in dollars)

1.0 0.25

4.0 1.00
Create an equation to represent the cost, y, in dollars, for x pounds of grain.

Answer 1

a.
`(1,0.25)`

b.
`y = 0.25x`

Explanation:

Given

The data in the table

Solving (a): The coordinate that represents the unit rate

The unit rate is when its 1 pound

This is so because the unit rate is dollars per pounds.

Hence, the coordinate is
`(1,0.25)`

Solving (b): Equation of the graph

First, we calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

Where:

`(x_1,y_1) = (1,0.25)`

`(x_2,y_2) = (4,1.00)`

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (1.00 - 0.25)/(4 - 1)`

`m = (0.75)/(3)`

`m = 0.25`

The equation is then calculated as thus:

`y - y_1 = m(x - x_1)`

This gives:

`y - 0.25 = 0.25(x - 1)`

`y - 0.25 = 0.25x - 0.25`

Make y the subject

`y = 0.25x`

Hence, the equation of the graph is:
`y = 0.25x`