Question

Paula has a large ball of yarn that she is going to use to knit a scarf for the winter. Every square inch on the scarf requires a certain number of yards of yarn from the ball. A linear model of this situation contains the values (11 , 352.99) and (30 , 126.7), where x represents the number of square inches knitted on the scarf, and y represents the number of yards remaining on the ball of yarn. How many yards of yarn did Paula start with?

Answer 1

She started with 484 yarns

Explanation:

Given

`(x_1,y_1) = (11,352.99)`

`(x_2,y_2) = (30,126.7)`

Required

Number of yarns she started with

The interpretation of this question is to calculate the y intercept.

We strt by calculating the slope (m)

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

`m = (352.99 - 126.7)/(11 - 30)`

`m = (226.29)/(-19)`

`m = -11.91`

Next, we calculate the linear equation as follows;

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

Where

`(x_1,y_1) = (11,352.99)`

`m = -11.91`

`y - 352.99 = -11.91(x - 11)`

`y - 352.99 = -11.91x + 131.01`

Make y the subject

`y= -11.91x + 131.01 + 352.99`

`y= -11.91x +484`

A linear equation has the form

`y=mx + b`

Where

`b = y\ intercept`

By comparison.

`b = 484`

Hence, she started with 484 yarns