Look at this table:
x y
–
3
–
33
–
2
–
25
–
1
–
17
0
–
9
1
–
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 given data follows a linear or exponential pattern, let's plot the points on a graph.
Here is the graph of the data:
x | y
-3 | -
33
-2 | -
25
-1 | -
17
0 | -
9
1 | -
1
It appears that the data follows a linear pattern. The points seem to lie on a straight line.
To find the equation of the line, we need to determine the slope (m) and the y-intercept (b).
Using two points from the table, let's calculate the slope:
m = (y2 - y1) / (x2 - x1)
Using the points (-3, 33) and (1, -1):
m = (-1 - 33) / (1 - (-3)) = -34 / 4 = -8.5
Now that we have the slope, we can find the y-intercept (b) by substituting the values of any point (x, y) into the equation y = mx + b.
Using the point (0, -9):
-9 = -8.5(0) + b
-9 = b
So the equation of the line that models the data is:
y = -8.5x - 9