# What is the slope of the line between (3,5) and (1, 3 )?

Nov 23, 2015

$1$

#### Explanation:

If a line passes through two points $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$ then its slope $m$ is given by the formula:

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

In our example, I would normally pick the points in the reverse order to the one you have specified in order to be working with positive numbers, like so:

$\left({x}_{1} , {y}_{1}\right) = \left(1 , 3\right)$

$\left({x}_{2} , {y}_{2}\right) = \left(3 , 5\right)$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{5 - 3}{3 - 1} = \frac{2}{2} = 1$

To demonstrate the the order of the points makes no difference to the result, let's see that with the points the other way round:

$\left({x}_{1} , {y}_{1}\right) = \left(3 , 5\right)$

$\left({x}_{2} , {y}_{2}\right) = \left(1 , 3\right)$

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{3 - 5}{1 - 3} = \frac{- 2}{- 2} = 1$