Question

In 2009, U.S. families, on average, spent $541.25 on back-to-school supplies. In 2016, the figure rose to $681.25. a. Find a linear model in the form, y=mx+b, that fits this data using x=0 to stand for the year 2000? b. Use your model or perhaps another algebraic idea to predict the back-to-school cost in the year 2025?

Answer 1

The linear model representing the back-to-school costs is y = 16x + 541.25. The predicted back-to-school cost in the year 2025 is $1441.25.

Step-by-step explanation:

To find the linear model in the form y = mx + b, we need to first find the slope (m) and the y-intercept (b) using the given data points. We have two data points: (0, 541.25) and (16, 681.25). The slope can be found using the formula:

m = (y2 - y1) / (x2 - x1)

m = (681.25 - 541.25) / (16 - 0) = 16

Now, we can substitute one of the data points into the equation y = mx + b to find the y-intercept. Let's use the point (0, 541.25):

541.25 = 16(0) + b

b = 541.25

Therefore, the linear model is: y = 16x + 541.25

To predict the back-to-school cost in the year 2025, we need to substitute x = 25 into the linear model:

y = 16(25) + 541.25 = 900 + 541.25 = 1441.25

So, the predicted back-to-school cost in the year 2025 is $1441.25.