# What is the slope of the line passing through the following points: (4,-1) , (-5, 2) ?

Mar 24, 2016

Slope (gradient) is $- \frac{1}{3}$

#### Explanation:

Slope (proper name is gradient) is the amount of change up or down for a given amount of change along.

These numbers are viewed reading from left to right.

If the slope is positive that the gradient is upwards.
If the slope is negative then the gradient is downwards.

Let $P$ be any point on the line

${P}_{1} \to \left({x}_{1} , {y}_{1}\right) \to \left(4 , - 1\right)$
${P}_{2} \to \left({x}_{2} , {y}_{2}\right) \to \left(- 5 , 2\right)$

Gradient $\to \left(\text{change in y-axis")/("change in x-axis}\right)$

$\text{Gradient } \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \to \frac{2 - \left(- 1\right)}{- 5 - 4} = \frac{3}{- 9} = - \frac{1}{3}$

The gradient is negative so the slope is downwards reading left to right.

So for 3 along you go down 1. Rather like the downward slope of a hill.