What is the equation of a line parallel to the line 3y + 4x = 15? *

Answer 1

standard form of linear equation is y = mx + b where m is gradient, b is y intercept.

rearrange 3y + 4x = 15 to get 3y = -4x + 15 then y = (-4/3)x + 5

m = (-4/3) b = 5 hence gradient is -4/3 (negative down and to the right, steeper than 45 degrees, 4 down, 3 across)

parallel lines must have the same gradient

hence, the general equation of parallel lines in this case is y = (-4/3)x + n

and a specific example (of infinite possibilities) could be y = (-4/3)x + 1/3 which is equivalent to 3y = 1 - 4x

and finally double-check your work to make sure derived equation is parallel to given line!