Question

Write a linear equation that represents the cost of buying T-shirts from Paula’s Printing. Identify the meaning of each variable in your equation.

Answer 1

`y=21.50x`

Explanation:

Let

x ----> the number of t-shirts

y ----> the cost of buying T-shirts from Paula’s Printing in dollars

take two points from the given data

we have

(2,43) and (4,86)

step 1

Find the slope

The formula to calculate the slope between two points is equal to

`m=(y2-y1)/(x2-x1)`

substitute the values in the formula

`m=(86-43)/(4-2)`

`m=(43)/(2)=\$21.50\ per\ t-shirt`

step 2

Find the equation of the line in point slope form

`y-y1=m(x-x1)`

we have

`m=21.50`

`(x1,y1)=(2,43)`

substitute

`y-43=21.50(x-2)`

step 3

Convert to slope intercept form

`y=mx+b`

Isolate the variable y

`y-43=21.50x-43`

`y=21.50x-43+43`

`y=21.50x`

This linear equation represent a proportional relationship (the line passes through the origin)