Look at this table:
x y
–
7
–
20
–
6
–
17
–
5
–
14
–
4
–
11
–
3
–
8
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether a linear function or an exponential function should be used to model the data, we can plot the given points on a graph and analyze their pattern.
$x$: -7, -6, -5, -4, -3
$y$: -20, -17, -14, -11, -8
Based on the pattern of the points, it appears that a linear function would best model the data.
To find the linear function, we need to calculate the slope, m, and the y-intercept, b.
We can calculate the slope using the formula:
m = (change in y) / (change in x)
From the first point to the last point, there is a change in y of -8 - (-20) = 12, and a change in x of -3 - (-7) = 4.
So, the slope m = 12 / 4 = 3.
Next, we can calculate the y-intercept, b, using the formula:
b = y - mx
Using any of the given points, let's use the first point (-7, -20):
b = -20 - 3(-7)
= -20 + 21
= 1
Therefore, the linear function that models the data is:
y = 3x + 1