# Can you find an equation parallel or perpendicular to a line when it is not in slope intercept form?

For example, if I need to find the equation of the line parallel to $$2x-3y=4$$ which passes through the point $$(1,-5)$$ I know how to do this by putting it into slope-intercept form first to find the slope and then plugging in the point to find the y-intercept.

Same thing for finding a line perpendicular to that point. I just wanted to know if I could do this without changing it into slope intercept form first

The slope of this line is $${2\over 3}$$ so the slope of perpendicular is $$-{3\over 2}$$ so the equation of perpenicular is $$y-(-5)= -{3\over 2}(x-1)$$
and the line parallel has the same slope, so $${2\over 3}$$ an thus it equation is $$y-(-5)= {2\over 3}(x-1)$$
• thank you! so then I would have $y+5 = 2/3(x-1)$ but what about if i wanted it in the same for that it was given on top. so i want the answer to be in the form $2x-3y=4$. I know I can manipulate what I have to get it there but is there a way to get there directly? May 18, 2019 at 17:31
Simply substitute $$x=1$$ and $$y=-5$$ in $$2x-5y$$ to get $$17$$. Hence the equation of the line parallel to $$2x-3y=4$$ passing through $$(1,-5)$$ is $$2x-5y=17$$.
For the perpendicular line plug in the coordinates $$(1,-5)$$ in $$3x+2y$$ to get $$3x+2y=-7$$.