# How do you find the slope given (0,1) and (3,-1)?

Jun 24, 2016

$- \frac{2}{3}$

#### Explanation:

The slope is the amount of up or down for the amount of along.

so slope (gradient) $\to \left(\text{change in y")/("change in x}\right)$

Let point 1 be ${P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(0 , 1\right)$
Let point 2 be${P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(3 , - 1\right)$
Let gradient be $m$

$m \to \left(\text{change in y")/("change in x}\right) \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{\left(- 1\right) - 1}{3 - 0}$

$m = - \frac{2}{3}$

As the slope is negative it means that the graph goes down as you move from left to right.

So you move 3 along then 2 down $\to - \frac{2}{3}$