Look at this table:
x y
–
7
–
61
–
6
–
53
–
5
–
45
–
4
–
37
–
3
–
29
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
This table shows a pattern where the value of y decreases by 8 as the value of x increases by 1. Therefore, this can be modeled by a linear function.
To find the equation of the linear function, we need to find the slope (m) and the y-intercept (b).
The slope (m) can be found by taking the difference in y-values (change in y) divided by the difference in x-values (change in x) for any two points.
Let's take the first two points (-7, 61) and (-6, 53):
m = (53 - 61) / (-6 - (-7))
m = (53 - 61) / (-6 + 7)
m = (-8) / 1
m = -8
Now that we have the slope (m), we can find the y-intercept (b) by substituting the values of any point (x, y) into the equation y = mx + b and solving for b.
Let's use the first point (-7, 61):
61 = -8(-7) + b
61 = 56 + b
b = 61 - 56
b = 5
Therefore, the linear function that models the data is:
y = -8x + 5