# What is the slope of the line passing through the following points:  (-3/4 , 2/3) , (1/3, 2/5 ) ?

May 28, 2017

$m = - \frac{16}{65} \approx - 0.2462$

#### Explanation:

The slope of a line passing through two points is given by the following slope formula:

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

We can plug in the values of the two points we have been given where

$\left({x}_{1} , {y}_{1}\right) = \left(- \frac{3}{4} , \frac{2}{3}\right)$

and

$\left({x}_{2} , {y}_{2}\right) = \left(\frac{1}{3} , \frac{2}{5}\right)$

The numerator of the slope formula is

${y}_{2} - {y}_{1} = \frac{2}{5} - \frac{2}{3} = \frac{2}{5} \frac{\times 3}{\times 3} - \frac{2}{3} \frac{\times 5}{\times 5} = \frac{6}{15} - \frac{10}{15} = - \frac{4}{15}$

The denominator of the slope formula is

${x}_{2} - {x}_{1} = \frac{1}{3} - \left(- \frac{3}{4}\right) = \frac{1}{3} + \frac{3}{4} = \frac{1}{3} \frac{\times 4}{\times 4} + \frac{3}{4} \frac{\times 3}{\times 3}$

$= \frac{4}{12} + \frac{9}{12} = \frac{13}{12}$

Finally, the slope formula is

$m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- \frac{4}{15}}{\frac{13}{12}} = - \frac{4}{15} \cdot \frac{12}{13} = - \frac{48}{195} = - \frac{16}{65}$