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:-
[tex](y-b)=\dfrac{b-d}{a-c}(x-a)[/tex]
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):
[tex](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)[/tex]
To find initial point, put x=0
[tex]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)[/tex]
Hence, Paula starts with 301.5 yarns.
