# How do you write the equation in point-slope form of the line passing through (4, 0) and (2, 6)?

##### 1 Answer
Apr 4, 2015

The Answer is : $\implies y - 6 = - 3 \left(x - 2\right)$ OR $y - 0 = - 3 \left(x - 4\right)$

The equation is of the form:

$y - {y}_{0} = m \left(x - {x}_{0}\right)$

where $m$ is the gradient and $\left({x}_{0} , {y}_{0}\right)$ is any point that lies on the line. So either of the points $\left(4 , 0\right)$ or $\left(2 , 6\right)$

Step 1: Find the gradient, m

$m = \frac{6 - 0}{2 - 4} = - 3$

Step 2: Write down the equation

$\implies y - 6 = - 3 \left(x - 2\right)$ taking $\left(2 , 6\right)$

or $y - 0 = - 3 \left(x - 4\right)$ taking $\left(4 , 0\right)$

Note that Both equations are correct as they all boil down to : $y = - 3 x + 12$ {This is the slope-intercept form}