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
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 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex] , where [tex](x_{1},y_{1})[/tex] and [tex](x_{2},y_{2})[/tex] 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)
∵ [tex]m=\frac{280-130}{8-2}=\frac{150}{6}=25[/tex]
∴ 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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