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

Mar 21, 2016

Slope (gradient )$\to - \frac{3}{5}$

#### Explanation:

Slope (gradient) is the amount of up or down for the amount of along. Like the incline on a hill.

Always read from left to right. If you go up reading left to right then it is a positive gradient. If you go down reading left to right then it is a negative gradient.

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

A memory jog could be "Why is this one on top".

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

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

Let gradient be $m$

Gradient$\textcolor{w h i t e}{.} \left(m\right) \to \left(\text{change in y-axis")/("change in x-axis}\right) \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{- 5 - \left(- 2\right)}{4 - \left(- 1\right)} = \frac{- 3}{5} = - \frac{3}{5}$

This is negative so for 5 along it goes down 3.