Look at this table:
x y
–
6
–
39.2
–
5
–
32.7
–
4
–
26.2
–
3
–
19.7
–
2
–
13.2
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
Based on the given data, we can see that the values of y decrease as x increases. Therefore, this data can be modeled by a linear function.
To find the equation of the linear function, we can determine the slope, m, and the y-intercept, b.
Slope (m) = (change in y) / (change in x)
(39.2 - 13.2) / (-5 - (-2)) = 26 / -3 = -8.67
The y-intercept (b) can be obtained by substituting the values of x and y into the linear equation and solving for b. Let's use the point (-2, 13.2):
13.2 = -8.67(-2) + b
13.2 = 17.34 + b
b = -4.14
Therefore, the linear function that models the data is:
y = -8.67x - 4.14