Look at this table:
x y
4
–
28.6
5
–
37.4
6
–
46.2
7
–
55
8
–
63.8
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the function that models the data is linear or exponential, we need to analyze the relationship between x and y.
Looking at the table, we can observe that as x increases by 1 unit, y increases by a constant amount. This suggests a linear relationship between x and y.
To find the linear function that models the data, we can find the slope (m) and y-intercept (b) using the given data points.
Taking the first two data points (4, 28.6) and (5, 37.4), we can calculate the slope using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
= (37.4 - 28.6) / (5 - 4)
= 8.8
Now that we have the slope, we can substitute it along with one of the points (e.g., (4, 28.6)) into the equation y = mx + b to solve for the y-intercept (b):
28.6 = 8.8(4) + b
b = 28.6 - 35.2
b = -6.6
Therefore, the linear function that models the data is:
y = 8.8x - 6.6