x y
–
5
–
1
–
4 0
–
3 1
–
2 2
–
1 3
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To determine whether a linear function or an exponential function would be a better model for the data, let's graph the given points and see if they follow a pattern.
Plotting the given data points, we get the following graph:
```
(5, 0)
(4, 1)
(3, 2)
(2, 3)
(1, 4)
```
Based on the graph, it appears that the data points follow a linear pattern instead of an exponential pattern. Therefore, a linear function would be a better model for the data.
To find the linear function, we can use the slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.
Let's find the slope (m) using two points on the line, (5, 0) and (1, 4):
m = (y2 - y1) / (x2 - x1)
= (4 - 0) / (1 - 5)
= 4 / (-4)
= -1
Now, let's substitute one point and the slope into the equation y = mx + b to solve for b:
0 = (-1)(5) + b
0 = -5 + b
b = 5
Therefore, the linear function that models the data is:
y = -x + 5