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 (12, 317.24) and (25, 164.75), 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? a. 458 b. 481.99 c. 495

A

Step-by-step explanation:

To find where Paula started, find the rate of change or slope in order to work backwards.

This means -11.73 yards remaining on the ball for each inch knitted. The first point is at (12, 317.24) so work backwards 12 inches or 12*11.73 = 140.76.

This means it started at 317.24 + 140.76 = 458.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

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