or
Look at this table:
x y
2 14
3 22
4 30
5 38
6 46
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the given data should be modeled with a linear or exponential function, we can analyze the relationship between the two variables.
Looking at the x-values, we can observe that they are increasing by a constant rate of 1. This suggests that the relationship is linear.
Now, let's take a look at the y-values. When the x-values increase by 1, the y-values increase by 8 (14, 22, 30, 38, 46). This indicates that the relationship between x and y is also linear, as the change in y is constant for each change in x.
To find the linear function that models the data, we need to determine the slope (m) and the y-intercept (b).
m = change in y / change in x
= (38 - 14) / (5 - 2)
= 24 / 3
= 8
To find the y-intercept, we can use one of the data points (2, 14):
y = mx + b
14 = 8(2) + b
14 = 16 + b
b = 14 - 16
b = -2
Therefore, the linear function that models the given data is:
y = 8x - 2