Answer:
[tex]y=\frac{3}{5} x+1[/tex] and [tex]5y=3x-2[/tex] are parallel.
[tex]10x-6y=-4[/tex] is neither parallel nor perpendicular.
Step-by-step explanation:
First, you have to simplify each equation in terms of y.
[tex]y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4[/tex]
Your first equation is already in terms of x, so simplify your second equation.
[tex]5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}[/tex]
Now you can simplify your third equation.
[tex]10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
These are your three equations in terms of y:
[tex]y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}[/tex]
Now, all you have to know is how to tell using your slope if a line is parallel or perpendicular to another.
Two parallel lines will have the exact same slope.
Two perpendicular lines will have slopes which are opposite reciprocals. For example, a line with a slope of 2 is perpendicular to a line with a slope of [tex]-\frac{1}{2}[/tex], as they have opposite signs and are reciprocal (2/1 versus 1/2) to each other.
Your first two equations have the same slope and are therefore parallel.
Your third equation is a reciprocal, but it is not opposite, and is therefore not parallel nor perpendicular.
