# Write an equation in point-slope form for the line through the given point (4,-6) with the given slope m=3/5?

Apr 3, 2015

$y = m x + c$

$- 6 = \left(4 \times \frac{3}{5}\right) + c$

$c = - \frac{12}{5} - 6 = - \frac{42}{5}$

So:

$y = \frac{3}{5} x - \frac{42}{5}$

Apr 3, 2015

The point slope form comes from the definition of slope as a measure of the change in $y$ for a given change in $x$ in passing from point 1 to point 2, i.e.:
slope$= m = \frac{\Delta y}{\Delta x} = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}}$...........(1).
The only difference here is that you do not have 2 points but only one!
So you have: the value of $m$ and the coordinates of one point, say, point 1. So we can write in (1):
$\frac{3}{5} = \frac{y - \left(- 6\right)}{x - 4}$ where the coordinates of the other point are the unknown $x , y$.
You get rearranging:
$y + 6 = \frac{3}{5} \left(x - 4\right)$
$y + 6 = \frac{3}{5} x - \frac{12}{5}$
$y = \frac{3}{5} x - \frac{12}{5} - 6$
$y = \frac{3}{5} x - \frac{42}{5}$