Question

Look at this table

x 1,2,3,4,5
y 2,1,0,-1,-2
Write a linear function (y= mx + b) or an exponential function (y=a(b)^x) that models the data.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since the data seems to show a linear pattern, a linear function is more appropriate to model the data.

To find the equation of the linear function using the given data points (1,2), (2,1), (3,0), (4,-1), and (5,-2), we can first calculate the slope (m) using two of the data points. Let's use the points (1,2) and (2,1) to calculate the slope:

m = (y2 - y1) / (x2 - x1)
m = (1 - 2) / (2 - 1)
m = -1

Now that we have the slope, we can use one of the points to find the y-intercept (b). Let's use the point (1,2):

2 = (-1)(1) + b
2 = -1 + b
b = 3

Therefore, the linear function that models the data is:
y = -x + 3