Abby bought yarn to knit a scarf for her mom, who requested it to be extra long. Now, Abby hopes she has enough yarn to meet that request.

There is a linear relationship between the length of the scarf, in inches, and the amount of yarn Abby has left, in yards.
Describe the rate of change for this relationship.
The amount of yarn left
by
per inch of scarf.

she starts of with 135 yards of yarn and she has 0 yards of yarn left with 70 inches of scarf

1 answer

To describe the rate of change in this linear relationship, we can analyze the yarn Abby has and the length of the scarf.

Abby starts with 135 yards of yarn and has left 0 yards after knitting a scarf that is 70 inches long. Based on this information, we can calculate the rate of change in terms of how much yarn is used per inch of scarf.

  1. Calculate the total amount of yarn used:

    • Initially, Abby has 135 yards and ends with 0 yards after knitting a 70-inch scarf.
    • Therefore, the total yarn used is: \[ 135 , \text{yards} - 0 , \text{yards} = 135 , \text{yards} \]
  2. Determine the amount of yarn used per inch:

    • Since 135 yards of yarn is used to knit a 70-inch scarf, we can determine the amount of yarn used per inch by dividing the total yarn used by the length of the scarf: \[ \text{Yarn used per inch} = \frac{135 , \text{yards}}{70 , \text{inches}} \approx 1.9286 , \text{yards per inch} \]

Thus, the rate of change for this relationship is approximately 1.93 yards per inch of scarf length. This means that for every inch of scarf Abby knits, she uses about 1.93 yards of yarn.