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 (20, 233) and (30, 114.5), 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

let  y = m x + c   be the linear relationship between the quantities.

    (20, 233) and  (30, 114.5)  lie on this straight line.
 
So   233 = 20 m + c
       114.5 = 30 m + c

Subtract the first from 2nd equation, to get:  10 m = - 118.5 
m = - 11.85
   Substitute this in the first equation:  233 = 20*(-11.85) + c
       So  c = 233+ 237 = 470 
 
So  y + 11.85 = 470    is the linear relationship.

Now     when knitting starts,  x = 0,  Hence  y = 470 yards
  She started with 470 yards