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

Jul 8, 2018

$\frac{1}{3}$

#### 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 $\left(1 , 1\right)$ and $\left(4 , 2\right)$.

We can find the slope of a line knowing two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$:

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{2 - 1}{4 - 1} = \frac{1}{3}$