Question

kim is saving monyfor a trip this summer. She already has some money in her savings account and will add the same amount to her account each week. At the end of 2 weeks, Carla has $130. At the end of 8 weeks, she has $280. Write a linear function in the form y = mx + b to represent the amount of money, m, that Carla has saved after w weeks.

Answer 1

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Step-by-step explanation:

Carla is saving money for a trip this summer. She already has some money in her savings account and will add the same amount to her account each week

• At the end of 2 weeks, Carla has $130
• At the end of 8 weeks, she has $280

Write a linear function in the form y = m x + b to represent the amount of money, m, that Carla has saved after w weeks

The linear equation is y = m x + b, where m is the slope of the line and b is the y-intercept

The formula of the slope is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$ , where $(x_{1},y_{1})$ and $(x_{2},y_{2})$ are 2 points on the line

∵ The slope is the rate of change of y and x

∴ The same amount of money that Carla add every week = m

∵ At the end of 2 weeks, Carla has $130

∴ The first point is (2 , 130)

∵ At the end of 8 weeks, she has $280

∴ The second point is (8 , 280)

∵ $m=\frac{280-130}{8-2}=\frac{150}{6}=25$

∴ The same amount of money that Carla add every week = $25

∵ The amount of money that Carla saved after w week is m

∴ m = 25 w + b, where b is the initial amount of money that she

   saved in her account

To find b substitute w and m by the coordinates of one of the two

given points, let us use the first point

∵ w = 2 and m = 130

∵ m = 25 w + b

∴ 130 = 25(2) + b

∴ 130 = 50 + b

- Subtract 50 from both sides

∴ 80 = b

∴ m = 25 w + 80

The linear function represents the amount of money, m, that Carla has saved after w weeks is m = 25 w + 80

Learn more:

You can learn more about the linear function in brainly.com/question/4326955

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