# What is the slope of the line passing through the following points:  (-3, 8), (1,6) ?

Feb 27, 2016

$m = - \frac{1}{2}$

#### Explanation:

To find the gradient (slope) of a line passing through 2 points

use the $\textcolor{b l u e}{\text{ gradient formula }}$

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

where$\left({x}_{1} , {y}_{1}\right) \text{ and " (x_2 , y_2 ) " are the coords of 2 points}$

here let$\left({x}_{1} , {y}_{1}\right) = \left(- 3 , 8\right) \text{ and } \left({x}_{2} , {y}_{2}\right) = \left(1 , 6\right)$

$\Rightarrow m = \frac{6 - 8}{1 - \left(- 3\right)} = \frac{- 2}{4} = - \frac{1}{2}$

Feb 27, 2016

$\textcolor{b l u e}{\text{The gradient of "-1/2" is negative meaning that the}}$$\textcolor{b l u e}{\text{ values are reducing}}$

#### Explanation:

Slope (gradient) is the amount of up or down for a given amount of along. Think of the slope of a hill!

So the gradient is

$\textcolor{b l u e}{\left(\text{change in up/down")/("change in along")" "->" "("change in the y-axis")/("change in the x-axis}\right)}$

You list (-3,8) first so we will take that as the starting point $\left({x}_{1} , {y}_{1}\right)$

Let $\left({x}_{1} , {y}_{1}\right) \text{ "->" } \left(- 3 , 8\right)$
Let $\left({x}_{2} , {y}_{2}\right) \text{ "->" } \left(1 , 6\right)$

$\text{ "("change in the y-axis")/("change in the x-axis")" "->" } \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For your question this gives:

$\text{ "(6-8)/(1 -(-3))" "=" "(-2)/4" "=" "-2/4" "=" } - \frac{1}{2}$

The negative gradient means that the graph 'goes down' as you move from left to right

$\textcolor{b l u e}{\text{The gradient of "-1/2" is negative meaning that the}}$$\textcolor{b l u e}{\text{values are reducing}}$