# How do you write an equation in point slope form given (5,-4), (1/2, -1/4)?

The equation of the line in slope-intercept form is $y = - \frac{5}{6} x + \frac{1}{6.}$
The slope of the line passing through $\left(5 , - 4\right) \mathmr{and} \left(\frac{1}{2} , - \frac{1}{4}\right)$ is $m = \frac{{y}_{2} - {y}_{1}}{{x}_{2} - {x}_{1}} = \frac{- \frac{1}{4} + 4}{\frac{1}{2} - 5} = \frac{\frac{15}{4}}{- \frac{9}{2}} = - \frac{5}{6}$
Let the equation of the line in slope-intercept form be $y = m x + c \mathmr{and} y = - \frac{5}{6} x + c$ The point (5,-4) will satisfy the equation . So, $- 4 = - \frac{5}{6} \cdot 5 + c \mathmr{and} c = \frac{25}{6} - 4 = \frac{1}{6}$
Hence the equation of the line in slope-intercept form is $y = - \frac{5}{6} x + \frac{1}{6.}$ graph{-5/6x+1/6 [-10, 10, -5, 5]}[Ans]