# How do you write the point-slope form of an equation of the line that passes through each pair of points (4,1), (-3,6)?

point-slope form: $y - {y}_{1} = m \left(x - {x}_{1}\right) m = \left[s l o p e\right] \left(h \texttt{p} : / s o c r a t i c . \mathmr{and} \frac{g}{a} l \ge b r \frac{a}{g} r a p h s - o f - l \in e a r - e q u a t i o n s - \mathmr{and} - f u n c t i o n \frac{s}{s} l o p e\right) \mathmr{and} \left({x}_{1} , {y}_{1}\right)$ is the point
slope-intercept form: $y = m x + c$
m(slope)=$\tan \theta = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{6 - 1}{- 3 - 4} = - \frac{5}{7}$
$\implies$7y-7= -5x+20
$\implies$ 5x+7y-27=0