# How do you find the point-slope form of the equation of the line passing through the points (8,11), (6,16)?

May 30, 2015

First we have to find the slope of the equation. To find the slope we have to do;
$\frac{y 2 - y 1}{x 2 - x 1}$ For our question slope is;

$\frac{16 - 11}{6 - 8} = \frac{5}{-} 2 = - \frac{5}{2}$

The main formula of a line is;
$y = a x + b$

We should use one point to find the real equation. If we use (6,16) point;
$y = a x + b \implies 16 = 6 a + b$;
a is the slope of the equation, we found that as $- \frac{5}{2}$;
$16 = \left(6 \cdot - \frac{5}{2}\right) + b \implies 16 = - 15 + b \implies b = 31$;
So the equation of the line will be;
$y = a x + b \implies \underline{y = - \frac{5}{2} x + 31}$
We can check if our equation is right or not with other given point;
$\left(8 , 11\right) \implies y = - \frac{5}{2} + 31 \implies 11 = \left(- \frac{5}{2} \cdot 8\right) + 31 \implies 11 = - 20 + 31 \implies 11 = 11$
So the equation is correct :)