Find parallel line to an equation when given pts, I've done an equation but I'm not sure if I did it correctly

I'm not really understanding how to find parallel lines (and perpindicular, but since the only difference is instead of using M I use -1/M, so if I find one I find the other)





Could someone please have a look at this, and tell me if I'm doing this right, or what I'm doing wrong (The answer looks feasable, but I have no way of checking)





Find the equation of the line parallel to 2x + 3y = 11 going through (2, 1)





Rearrange 2x + 3y = 11 to find the gradient





3y = 11 – 2x





To divide the 3y by 3 (to find y) I divided both of the other equations by 3.


y = -2/3 * x + 11/3





Because y=gradient (m)* x+c the gradient is -2/3.





Parallel lines have the same gradient, and I know the new line goes through point (2, -1) so I can put this into the above equation:


-1 = -2/3 * 2 + c





-1 = 4/3 + c


-1--4/3 = 1/3


so c = 1/3





Substituted:


y=-2/3 x + 1/3

Find parallel line to an equation when given pts, I've done an equation but I'm not sure if I did it correctly
If the 'going thru' point is (2, -1), then your equation is correct.





However, you were given point (2, 1), in which case the





c = 7/3





y = - 2/3x + 7/3
Reply:...i cant be of much help because i dont remember the stuff very well.....but a little trick i used to use was graphing them on a graphing calculator.....if the lines look close to parallel or perpendicular, you'r probably right...
Reply:yes im pretty sure you did that correctly...i did it myself and got the same thing and then i checked it on a graphing calculator.