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

May 22, 2016

$\frac{\sqrt{5} - \sqrt{3}}{2}$

#### 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 $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$. 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 $f \left(3\right) = \sqrt{3}$. For $x = 5$, the $y$ value is $f \left(5\right) = \sqrt{5}$.

Thus, the secant line's slope is $\frac{\sqrt{5} - \sqrt{3}}{5 - 3} = \frac{\sqrt{5} - \sqrt{3}}{2} \approx 0.2520$.

We can formalize this all by saying that the slope of secant line passing through $x = a$ and $x = b$ is equal to $\frac{f \left(b\right) - f \left(a\right)}{b - a}$.