Answer and Explanation:
In this problem, we need to find the slope of the secant lines of the function y = √x that go through the points:
- line 1: (0, 0) and (4, 2)
- line 2: (0, 0) and (9, 3)
- line 3: (0, 0) and (16, 4)
We can use the following formula for slope (m):
m = rise / run
m = Δy / Δx
Line 1
m = 2 / 4 = 1/2
Line 2
m = 3 / 9 = 1/3
Line 3
m = 4 / 16 = 1/4
Further Note
We can see that the average rate of change, or slope of a secant line that goes through the origin, of the function y = √x decreases as x increases.