Answer:
and
are parallel.
is neither parallel nor perpendicular.
Step-by-step explanation:
First, you have to simplify each equation in terms of y.
![y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B5%7D%20x%2B1%5C%5C5y%3D3x-2%5C%5C10x-6y%3D-4)
Your first equation is already in terms of x, so simplify your second equation.
![5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}](https://tex.z-dn.net/?f=5y%3D3x-2%5C%5Cy%3D%5Cfrac%7B3%7D%7B5%7D%20x-%5Cfrac%7B2%7D%7B5%7D)
Now you can simplify your third equation.
![10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}](https://tex.z-dn.net/?f=10x-6y%3D-4%5C%5C-6y%3D-10x-4%5C%5Cy%3D%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B2%7D%7B3%7D)
These are your three equations in terms of y:
![y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B5%7D%20x%2B1%5C%5C%5C%5Cy%3D%5Cfrac%7B3%7D%7B5%7D%20x-%5Cfrac%7B2%7D%7B5%7D%20%5C%5C%5C%5Cy%3D%5Cfrac%7B5%7D%7B3%7D%20x%2B%5Cfrac%7B2%7D%7B3%7D)
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
, 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.