y = 3/5x + 1, 5y = 3x - 2, 10x - 6y = -4is it perpendicular, parallel, neither

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.