# What is the slope of (-23,4) and (-4, 5)?

Feb 6, 2015

The slope is a number that tells you how $y$ varies when $x$ varies and basically gives you the INCLINATION of the line, in this case, in between two points.

To evaluate this number you simply look at the change in $y$ divided by the change in $x$ or:

$s l o p e = m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$m = \frac{5 - 4}{- 4 - \left(- 23\right)} = \frac{1}{19}$
or starting from the other point:
$m = \frac{\left(4\right) - 5}{- 23 - \left(- 4\right)} = \frac{- 1}{-} 19 = \frac{1}{19}$

Which is a positive number meaning that your line is inclined upwards, i.e., when $x$ increases also $y$ increases (in particular, when $x$ increase of $1$ units $y$ increases of $\frac{1}{19}$).

Graphically:

hope it helps