what is an equation in point slope form that is perpendicular to 3x-5y=10 and goes through the point (2,-1)

Answer 1

3x -5y = 10, 5y = 3x-10, y = 3x/5 - 2, slope = 3/5

perpendicular line has slope=-5/3, the negative inverse

y=-5x/3 +b, to solve for b, plug in x=2, y=-1

-1 = -5(2)/3 +b

b = -1+10/3 = -3/3 +10/3 = 7/3

y= -5x/3 +7/3 is the perpendicular line through the given point, in slope intercept form

or

3y =-5x+7

or

5x +3y -7 = 0 in general form

or

5x +3y = 7 in standard form

it helps to do at least a rough graph of the lines and point