# What is the slope of the line between (6,9) and (18, -2 )?

Nov 17, 2015

The gradient is $\textcolor{w h i t e}{\times} \textcolor{b l u e}{- \frac{11}{12}}$.

As it is a negative slope it shows that it's gradient is downwards as you move from left to right.

#### Explanation:

Put in simple terms: It is the amount of 'up or down' for one along.

Let the gradient (slope) be m

Note the positive gradient is an upwards slope whilst a negative gradient is a downward one.

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

The negative 2 has been highlighted in blue. Subtracting or adding negative numbers needs a bit more care!
$\left({x}_{1} , {y}_{1}\right) \to \left(6 , 9\right)$
$\left({x}_{2} , {y}_{2}\right) \to \left(18 , \textcolor{b l u e}{- 2}\right)$

$m = \frac{\textcolor{b l u e}{- 2} - 9}{18 - 6}$

$m = - \frac{11}{12}$

It is more precise to keep this as a fraction.