What is the slope of the line passing through the following points:  (-5, 4) ,(7, -2) ?

Mar 14, 2016

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

Explanation:

Slope is defined as $\frac{\Delta y}{\Delta x}$ . In other words, it is the change in $y$ over the change in $x$. When we have two points, we can calculate the slope by subtracting the corresponding values and making them into a ratio.

$x - y$ coordinate points are in the form $\left(x , y\right)$
We have $\left(- 5 , 4\right)$ and $\left(7 , - 2\right)$
Let's call $\left(- 5 , 4\right) = \left({x}_{1} , {y}_{1}\right)$ and $\left(7 , - 2\right) = \left({x}_{2} , {y}_{2}\right)$
Now, it doesn't matter which point you choose to subtract from which point- it will work either way, as you can see below when calculating the slope:

$\frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- 2 - 4}{7 - - 5} = \frac{- 2 - 4}{7 + 5} = \frac{- 6}{12} = - \frac{1}{2}$

Is equivalent to the other way around:

$\frac{\Delta y}{\Delta x} = \frac{{y}_{1} - {y}_{2}}{{x}_{1} - {x}_{2}} = \frac{4 - - 2}{- 5 - 7} = \frac{4 + 2}{- 5 - 7} \frac{6}{-} 12 = - \frac{1}{2}$

Just make sure you are consistent in the order you subtract.