For this case we have that by definition, the equation of a line of the point-slope form is given by:
![y-y_ {0} = m (x-x_ {0})](/tpl/images/0381/8186/3a0bc.png)
Where:
m: It's the slope
It is a point through which the line passes
To find the slope, we need two points through which the line passes, observing the image we have:
![(x_ {1}, y_ {1}): (1,6)\\(x_ {2}, y_ {2}): (5, -2)\\m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-2-6} {5-1} = \frac {-8} {4} = -2](/tpl/images/0381/8186/9cafb.png)
Thus, the equation is of the form:
![y-y_ {0} = - 2 (x-x_ {0})](/tpl/images/0381/8186/2f1c1.png)
We choose a point:
![(x_{0}, y_ {0}) :( 5, -2)](/tpl/images/0381/8186/ab12a.png)
Finally, the equation is:
![y - (- 2) = - 2 (x-5)\\y + 2 = -2 (x-5)](/tpl/images/0381/8186/90638.png)
![y + 2 = -2 (x-5)](/tpl/images/0381/8186/d6160.png)