# How do you find the point-slope form of the equation of the line passing through the points (–1, –3) and (4, 1)?

Mar 30, 2015

Slope equals change in $y$ divided by the change in $x$
or stated equivalently
$m = \frac{\Delta y}{\Delta x}$

For this example
$m = \frac{1 - \left(- 3\right)}{4 - \left(- 1\right)} = \frac{4}{5}$

The slope point formula is
$\left(y - {y}_{0}\right) = m \left(x - {x}_{0}\right)$
and we may use either of the given points for (x_0,y_0)

Suppose we choose $\left({x}_{0} , {y}_{0}\right) = \left(4 , 1\right)$

Then the slope-point formula is
$y - 1 = \frac{4}{5} \left(x - 4\right)$
simplifying:
$5 y - 5 = 4 x - 16$
or
$5 y - 4 x = - 11$