Look at this table:
x y
–
7 34.68
–
6 29.68
–
5 24.68
–
4 19.68
–
3 14.68
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the function is linear or exponential, we can look at how the y-values change as the x-values change.
If the y-values change by a constant amount for each unit change in x, then the function is linear.
If the y-values change by a constant factor for each unit change in x, then the function is exponential.
Looking at the given data, we can see that as the x-values increase by 1, the y-values decrease by a constant amount of 5. So, the function is linear.
To find the linear function, we can use the formula y = mx + b, where m is the slope (change in y over change in x) and b is the y-intercept (the y-value when x is 0).
Using the first two data points, we can calculate the slope:
m = (y2 - y1) / (x2 - x1)
= (29.68 - 34.68) / (-6 - (-7))
= (-5) / (1)
= -5
Now, we can choose either of the points to find the y-intercept. Let's use the first point (x = -7, y = 34.68):
34.68 = (-5)(-7) + b
34.68 = 35 + b
b = 34.68 - 35
b = -0.32
Thus, the linear function that models the given data is:
y = -5x - 0.32