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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 (11 , 352.99) and (30 , 126.7), 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?

Respuesta :

MrRoyal

Answer:

She started with 484 yarns

Step-by-step explanation:

Given

[tex](x_1,y_1) = (11,352.99)[/tex]

[tex](x_2,y_2) = (30,126.7)[/tex]

Required

Number of yarns she started with

The interpretation of this question is to calculate the y intercept.

We strt by calculating the slope (m)

[tex]m = \frac{y_1 - y_2}{x_1 - x_2}[/tex]

[tex]m = \frac{352.99 - 126.7}{11 - 30}[/tex]

[tex]m = \frac{226.29}{-19}[/tex]

[tex]m = -11.91[/tex]

Next, we calculate the linear equation as follows;

[tex]y - y_1 = m(x - x_1)[/tex]

Where

[tex](x_1,y_1) = (11,352.99)[/tex]

[tex]m = -11.91[/tex]

[tex]y - 352.99 = -11.91(x - 11)[/tex]

[tex]y - 352.99 = -11.91x + 131.01[/tex]

Make y the subject

[tex]y= -11.91x + 131.01 + 352.99[/tex]

[tex]y= -11.91x +484[/tex]

A linear equation has the form

[tex]y=mx + b[/tex]

Where

[tex]b = y\ intercept[/tex]

By comparison.

[tex]b = 484[/tex]

Hence, she started with 484 yarns

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