# How to find the slope of a line containing (8,5) (-4,7)?

Apr 7, 2015

Given any two points on a straight line, $\left({x}_{1} , {y}_{1}\right)$ and $\left({x}_{2} , {y}_{2}\right)$
the slope is defined as
$\frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

For the given points $\left(8 , 5\right)$ and $\left(- 4 , 7\right)$
we have
slope $= \frac{7 - 5}{\left(- 4\right) - 8} = \frac{2}{- 12} = - \frac{1}{6}$

Apr 7, 2015
• color(green)(Slope= (Rise)/(Run)

The $R i s e$ is the Difference of the Y coordinates of any two points on the line
And the $R u n$ is the Difference of the X coordinates of those two points

• If the coordinates of the points are $\left({x}_{1} , {y}_{1}\right) \mathmr{and} \left({x}_{2} , {y}_{2}\right)$, then $\left[S l o p e\right] \left(h \texttt{p} : / s o c r a t i c . \mathmr{and} \frac{g}{a} l \ge b r \frac{a}{g} r a p h s - o f - l \in e a r - e q u a t i o n s - \mathmr{and} - f u n c t i o n \frac{s}{s} l o p e\right) = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$
Here, the coordinates are $\left(8 , 5\right)$ and $\left(- 4 , 7\right)$

$S l o p e = \frac{7 - 5}{- 4 - 8} = \frac{2}{-} 12 = - \frac{1}{6}$

The slope of the line passing through points $\left(8 , 5\right)$ and $\left(- 4 , 7\right)$ is color(green)(-1/6

• The graph of the line will look like this:

graph{y=(-x/6)+(38/6) [-16.01, 16.02, -8, 8.03]}