The table shows a function. Is the function linear or nonlinear?
x y
0 20
15 5
20 0
The function is linear because there is a constant rate of change between the x-values and the y-values.
To determine if the function is linear or nonlinear, we need to examine the relationship between the x-values and the y-values.
In a linear function, the ratio of change in y to change in x, also known as the slope, remains constant. If the slope changes, then the function is nonlinear.
Let's calculate the slope between the first two points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (5 - 20) / (15 - 0)
Slope = (-15) / 15
Slope = -1
Now, let's calculate the slope between the last two points:
Slope = (y2 - y1) / (x2 - x1)
Slope = (0 - 5) / (20 - 15)
Slope = (-5) / 5
Slope = -1
Since the slope between any two points is constant (-1), we can conclude that the function is linear.