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 (12, 317.24) and (25, 164.75), 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? A. 458 B. 481.99 C. 495

Answer 1

A. 458

Explanation:

Linear model equation:

y = m*x + h

where m is the slope of the line and h is the y-intercept.

Given 2 points (x1, y1) and (x2,y2) we can compute the slope as follows:

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

Replacing with (12, 317.24) and (25, 164.75):

m = (164.75 - 317.24)/(25 - 12) = -11.73

Replacing this value and point (12, 317.24) into the equation we get:

317.24 = -11.73*12 + h

h = 317.24 + 11.73*12

h = 458

then, the equation is y = -11.73*x + 458. At the beginning the number of square inches knitted is zero (x = 0) and the number of yards remaining is 458.

Answer 2

A

Explanation:

To find where Paula started, find the rate of change or slope in order to work backwards.

`m = (317.24 - 164.75)/(12-25) =(152.49)/(-13) = -11.73`

This means -11.73 yards remaining on the ball for each inch knitted. The first point is at (12, 317.24) so work backwards 12 inches or 12*11.73 = 140.76.

This means it started at 317.24 + 140.76 = 458.