Question

How do you find the slope of the secant lines of `y=sqrt(x)` through the points: x=1 and x=4?

Answer 1

`1/3`

Explanation:

Consider the function `y=sqrt(x)`. When `x=1,y=sqrt(x)=sqrt(1)=1`. In addition, when `x=4,y=sqrt(x)=sqrt(4)=2`.

Thus, the secant line should pass through the points `(1,1)` and `(4,2)`.

We can find the slope of a line knowing two points `(x_1,y_1)` and `(x_2,y_2)`:

`m=(y_2-y_1)/(x_2-x_1)=(2-1)/(4-1)=1/3`