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.

Step-by-step explanation:

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

$(y-b)=\dfrac{b-d}{a-c}(x-a)$

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):

$(y-300.2)=\dfrac{26-15}{177.88-300.2}(x-15)\\\\\Rightarrow (y-300.2)=\dfrac{11}{-122.32}(x-15)\\\\\Rightarrow (y-300.2)=\dfrac{11}{-122.32}(x-15)$

To find initial point, put x=0

$y-300.2=-\dfrac{11}{122.32}(0-15)\\\\\Rightarrow\ y-300.2=\dfrac{375}{278}\\\\\Rightarrow\ y=\dfrac{375}{278}+300.2\\\\\Rightatrrow\ y=301.5 \ \ (approx)$

Hence, Paula starts with 301.5 yarns.