To determine whether the function is linear or exponential, we need to find the difference in y-values between each pair of data points. If the differences are consistent, then the function is linear; if the ratios are consistent, then the function is exponential.
Let's find the differences in y-values:
-10: 73
-9: 65
-8: 57
-7: 49
-6: 41
Differences:
73 - 65 = 8
65 - 57 = 8
57 - 49 = 8
49 - 41 = 8
The differences in y-values are consistent, indicating that the function is linear. Now we need to find the slope (m) and the y-intercept (b) for the linear function y=mx+b.
First, calculate the slope:
m = (65-41) / (-9-(-6)) = 8 / -3 = -8/3
Next, substitute one of the points into the equation to find the y-intercept:
73 = (-8/3)(-10) + b
73 = 80/3 + b
73 - 80/3 = b
(219 - 80) / 3 = b
139 / 3 = b
b = 46.33
Therefore, the linear function that models the data is:
y = (-8/3)x + 46.33
look at this table:
x
-10
-9
-8
-7
-6
y
73
65
57
49
41
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
1 answer