# What is the equation in point-slope form of the line passing through (2, 5) and (–1, 8)?

May 30, 2015

$y = - x + 7$

#### Explanation:

First, we have to find the slope of the equation. To find the slope we have to do;

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

For our question slope is;

$m = \frac{8 - 5}{- 1 - 2} = \frac{3}{-} 3 = - 1$

The equation of a line is;

$y = a x + b$

We should use one point to find the real equation. If we use $\left(2 , 5\right)$ point;

$y = a x + b \implies 5 = 2 a + b$

$a$ is the slope of the equation, we found that as $- 1$;

$5 = 2 \cdot \left(- 1\right) + b \implies 5 = - 2 + b \implies b = 7$

So the equation of the line will be;

$y = a x + b \implies y = - x + 7$

We can check if our equation is right or not with other given point;

$\left(- 1 , 8\right) \implies y = - x + 7 \implies 8 = - \left(- 1\right) + 7 \implies 8 = 8$