Look at this table:
x y
–
8
–
55.1
–
7
–
48.1
–
6
–
41.1
–
5
–
34.1
–
4
–
27.1
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the data is best modeled by a linear or exponential function, let's plot the points on a graph:
x | y
-8 | -
-7 | 55.1
-6 | 48.1
-5 | 41.1
-4 | 34.1
From the graph, it appears that the data follows a linear pattern. We can use the point-slope form of a linear equation, y = mx + b, to find the equation that models the data.
To find the slope (m), we can pick any two points and use the formula:
m = (y2 - y1) / (x2 - x1)
Let's use the points (-4, 34.1) and (-8, -) to find the slope:
m = (34.1 - -) / (-4 - -8)
m = (34.1 - -) / (-4 + 8)
m = (-)
m = -
To find the y-intercept (b), we can substitute any point and the slope (m) into the equation y = mx + b and solve for b. Let's use the point (-4, 34.1):
34.1 = (-) * -4 + b
34.1 = (-) + b
b = 34.1 + (-)
b =
Therefore, the linear function that models the data is:
y = -(x) +
(Note: The missing value should be filled in using the actual data or clarified information.)