Cual de las siguientes rectas son perpendiculares a la recta de la ecuación 4x+6y-6=0

Ok, i will answer in English.

The first step is to know that when we have a linear equation like:

y = a*x + b

any line with a slope equal to - 1/a will be perpendicular to our line.

So first let's write our equation in the standard form:

4x + 6y - 6 = 0

6y = - 4x + 6

y = (-2/3) * x + 1

then the slope is (-2/3)

then the slope of the perpendicular line will be:

- (1 / (-2/3)) = 3/2

So the only thing any line with the equation:

y = (3/2) * x + c

where c can be any real number, is perpendicular to 4x+6y-6=0