The table shows a function. Is the function linear or nonlinear?
x y
–10 3
–5 7
0 9
Based on the given data, we can determine if the function is linear or nonlinear by checking if the difference in y-values divided by the difference in x-values is constant.
For the first data point (-10, 3) and the second data point (-5, 7):
Difference in y: 7 - 3 = 4
Difference in x: -5 - (-10) = 5
4/5 = 0.8
For the second data point (-5, 7) and the third data point (0, 9):
Difference in y: 9 - 7 = 2
Difference in x: 0 - (-5) = 5
2/5 = 0.4
Since the ratio of the differences in each case is not constant, the function is nonlinear.
To determine if the function is linear or nonlinear, we need to check if there is a constant rate of change between any two points in the table.
Let's calculate the rate of change between the first two points:
(x1, y1) = (-10, 3)
(x2, y2) = (-5, 7)
Rate of change = (y2 - y1) / (x2 - x1)
= (7 - 3) / (-5 - (-10))
= 4 / 5
Now, let's calculate the rate of change between the second two points:
(x1, y1) = (-5, 7)
(x2, y2) = (0, 9)
Rate of change = (y2 - y1) / (x2 - x1)
= (9 - 7) / (0 - (-5))
= 2 / 5
Since the rate of change is different between the two pairs of points, the function is nonlinear.