Question

A linear model of this situation contains the values (15, 300.2) and (26, 177.88) 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

Answer: Paula starts with 301.5 yarns.

Explanation:

Equation of a line passing through two points (a,b) and (c,d) is given by:-

`(y-b)=(b-d)/(a-c)(x-a)`

Given: x= number of square inches knitted on the scarf

y= number of yarns remaining on the ball of yarn

The equation of a line passing through (15, 300.2) and (26, 177.88):

`(y-300.2)=(26-15)/(177.88-300.2)(x-15)\\\\\Rightarrow (y-300.2)=(11)/(-122.32)(x-15)\\\\\Rightarrow (y-300.2)=(11)/(-122.32)(x-15)`

To find initial point, put x=0

`y-300.2=-(11)/(122.32)(0-15)\\\\\Rightarrow\ y-300.2=(375)/(278)\\\\\Rightarrow\ y=(375)/(278)+300.2\\\\\Rightatrrow\ y=301.5 \ \ (approx)`

Hence, Paula starts with 301.5 yarns.