Question

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

Answer 1

Answer:

$y=\frac{3}{5} x+1$ and $5y=3x-2$ are parallel.

$10x-6y=-4$ is neither parallel nor perpendicular.

Step-by-step explanation:

First, you have to simplify each equation in terms of y.

$y=\frac{3}{5} x+1\\5y=3x-2\\10x-6y=-4$

Your first equation is already in terms of x, so simplify your second equation.

$5y=3x-2\\y=\frac{3}{5} x-\frac{2}{5}$

Now you can simplify your third equation.

$10x-6y=-4\\-6y=-10x-4\\y=\frac{5}{3} x+\frac{2}{3}$

These are your three equations in terms of y:

$y=\frac{3}{5} x+1\\\\y=\frac{3}{5} x-\frac{2}{5} \\\\y=\frac{5}{3} x+\frac{2}{3}$

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 $-\frac{1}{2}$, 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.