Question

is theses equations parallel or perpendicular or neither, 3y=2x+14, 2x-3y=2

Answer 1

First line equation is 3y = 2x+14

Divide by 3 to each side.

3y/3 = (2x+14)/3

y = 2x/3+14/3

y = (2/3)x+14/3

Slope of the first  line say m1 = 2/3.

Second line is2x-3y = 2

Subtract 2x from each side.

2x-2x-3y = 2-2x

-3y = 2-2x

Divide by nagitive 3 to each side.

-3y/-3 = (2-2x)/-3

y = 2/-3+2x/3

y = (2/3)x-2/3

Slope of the second line say m2 = 2/3

m1 = m2

slopes of the two lines are equal.

So the given lines are parallel lines.