# How do you write the equation of a line in point slope form and slope intercept form given points (2, 7) (1, -4)?

May 23, 2015

The slope of the line segment between two points is the change in $y$ divide by the change in $x$.

For the case of a line through $\left(2 , 7\right)$ and $\left(1 , - 4\right)$ we have

slope $m = \frac{\Delta y}{\Delta x} = \frac{- 4 - 7}{1 - 2} = - \frac{11}{-} 1 = 11$

Using the point $\left(2 , 7\right)$ we can write the equation of the line in point slope form as:

$y - 7 = m \left(x - 2\right)$ where the slope $m = 11$.

That is:

$y - 7 = 11 \left(x - 2\right)$

To get point intercept form, first expand the right hand side so...

$y - 7 = 11 x - \left(11 \cdot 2\right) = 11 x - 22$

Then add $7$ to both sides to get:

$y = 11 x - 15 = 11 x + \left(- 15\right)$

This is point intercept ( $y = m x + c$ ) form with slope $m = 11$ and intercept $c = - 15$.