How do you find the slope of the line passing through the points (1,6) and (10, -9)?

May 1, 2017

$\text{slope} = - \frac{15}{9}$

Explanation:

To find the slope, you need to use the following formula

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

Slope basically tells us a little about the line on our graph. How steep is it? Is it negative or positive? Is there a zero slope (horizontal line)?

You take whatever you are given and work with that to solve for the unknown. Here, we are given 2 points on a graph.

$\textcolor{w h i t e}{a a a a a a a a a a a a} \left(1 , 6\right)$
$\textcolor{w h i t e}{a a a a a a a a a a a a} \left(10 , - 9\right)$

The first number corresponds to the point on the $\text{x axis}$. The second number corresponds to the point on the $\text{y axis}$. We can arbitrarily decide which is our $\left({x}_{1} , {y}_{1}\right)$ and which is our $\left({x}_{2} , {y}_{2}\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a} \textcolor{red}{\left(1 , 6\right) \to \left({x}_{1} , {y}_{1}\right)}$
$\textcolor{w h i t e}{a a a a a a a a a a a a a} \textcolor{b l u e}{\left(10 , - 9\right) \to \left({x}_{2} , {y}_{2}\right)}$

$S l o p e = \frac{\Delta y}{\Delta x} \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} \to \left(\left(\textcolor{b l u e}{\text{-9"-color(red)"6"))/((color(blue)"10"-color(red)"1}}\right)\right) = \textcolor{\mathmr{and} a n \ge}{- \frac{15}{9}}$

$A n s w e r : \text{slope} = \textcolor{\mathmr{and} a n \ge}{- \frac{15}{9}}$