How do you find the slope given (8,17) and (14,-17)?

1 Answer
Jul 13, 2016

$- \frac{17}{3}$

Explanation:

Slope (gradient) $\to \left(\text{change in the y-axis")/("change in the x-axis}\right)$

Think of the gradient of a hill.

Let Point 1$\to {P}_{1} \to \left({x}_{1} , {y}_{1}\right) = \left(8 , 17\right)$

Let Point 2$\to {P}_{2} \to \left({x}_{2} , {y}_{2}\right) = \left(14 , - 17\right)$

Let the slope (gradient) be $m$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\to \left(\text{change in the y-axis")/("change in the x-axis}\right) \to \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$

$\implies m \text{ "=" "(-17-17)/(14-8)" "=" } \frac{- 34}{6}$

But $- \frac{34}{6} \text{ " =" " -(34-:2)/(6-:2)" " =" } - \frac{17}{3}$