# What is the slope of the line that goes through points (6,0) and (0, -8)?

Mar 3, 2018

$\setminus q \quad \setminus q \quad \text{slope of line between" \ ( 6, 0 ) \quad "and} \setminus \quad \left(0 , - 8\right) \setminus = \setminus \frac{4}{3} \setminus .$

#### Explanation:

$\text{Recall the definition of the slope of a line between two points: }$

$\setminus \quad \text{slope of line between" \ ( x_1, y_1 ) \quad "and} \setminus \quad \left({x}_{2} , {y}_{2}\right) \setminus = \setminus \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} .$

$\text{Applying this definition to our two given points, we get:}$

$\setminus \quad \text{slope of line between" \ ( 6, 0 ) \quad "and} \setminus \quad \left(0 , - 8\right) \setminus = \setminus \frac{\left(- 8\right) - \left(0\right)}{\left(0\right) - \left(6\right)}$

$\setminus q \quad \setminus q \quad \setminus q \quad \setminus q \quad = \setminus \frac{- 8}{- 6} \setminus = \setminus \frac{\left(- 2\right) \left(4\right)}{\left(- 2\right) \left(3\right)} \setminus = \setminus \frac{\textcolor{red}{\cancel{\left(- 2\right)}} \left(4\right)}{\textcolor{red}{\cancel{\left(- 2\right)}} \left(3\right)} \setminus = \setminus \frac{4}{3.}$

$\text{So, we conclude:}$

$\setminus q \quad \setminus q \quad \text{slope of line between" \ ( 6, 0 ) \quad "and} \setminus \quad \left(0 , - 8\right) \setminus = \setminus \frac{4}{3} \setminus .$