# How do you find the slope given (0,5) and (5/2,0)?

Jul 14, 2016

The slope equals $m = - \frac{1}{2}$

#### Explanation:

Slope which is the change in $x$ versus the change in $y$.

Slope is identified by the letter $m$

$m = \frac{\Delta y}{\Delta x}$

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

The y-intercept $\left(0 , 5\right)$ and x-intercept $\left(\frac{5}{2} , - 0\right)$

${x}_{1} = 0$
${y}_{1} = 5$
${x}_{2} = \frac{5}{2}$
${y}_{2} = 0$

$m = \frac{0 - \frac{5}{2}}{5 - 0}$

$m = \frac{- \frac{5}{2}}{5}$

To simplify multiply by the reciprocal of the denominator

$m = - \frac{\cancel{5}}{2} \cdot \frac{1}{\cancel{5}}$

The slope equals $m = - \frac{1}{2}$