# What is the slope of the line passing through (7, -2) and (4,-3). What is the rise of that slope?

Oct 29, 2016

The slope of this line is $\frac{1}{3}$, and the rise of this slope is $+ 1$.

#### Explanation:

Given two points on a line with coordinates $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$, the slope of the line, $m$, is found using the formula

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

Since we have two points $\left(7 , - 2\right)$ and $\left(4 , - 3\right)$, we can substitute these coordinates into the slope formula and simplify the expression to obtain the slope of this line.

$m = \frac{- 3 - - 2}{4 - 7} = \frac{- 1}{- 3} = \frac{1}{3}$

So the slope of the line is $\frac{1}{3}$.

As for the second question, slope is often defined as "rise over run." Therefore the 'rise' of this slope is $+ 1$.