Question

How do you find the slope of the secant lines of `f(x) =sqrtx` through the points: [3, 5]?

Answer 1

`(sqrt5-sqrt3)/2`

Explanation:

We have two points: one that passes through the point on the function at `x=3`, and the other which passes through the function at `x=5`.

The slope of the line is found through `m=(y_2-y_1)/(x_2-x_1)`. Here, our `x` values are `3` and `5`, and our `y` values are the function values for these.

The `y` value for `x=3` is `f(3)=sqrt3`. For `x=5`, the `y` value is `f(5)=sqrt5`.

Thus, the secant line's slope is `(sqrt5-sqrt3)/(5-3)=(sqrt5-sqrt3)/2approx0.2520`.

We can formalize this all by saying that the slope of secant line passing through `x=a` and `x=b` is equal to `(f(b)-f(a))/(b-a)`.