# How do you determine if 5y+3x=1  is parallel, perpendicular to neither to the line y+10x=-3?

Nov 5, 2014

Let us rewrite them in Slope-Intercept Form, which essentially means that we solve for $y$.

Line 1: $5 y + 3 x = 1$

by subtracting $3 x$,

$\implies 5 y = - 3 x + 1$

by dividing by $5$,

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

So, the slope is ${m}_{1} = - \frac{3}{5}$.

Line 2: $y + 10 x = - 3$

by subtracting $10 x$,

$\implies y = - 10 x - 3$

So, the slope is ${m}_{2} = - 10$.

Since ${m}_{1} \ne {m}_{2}$, they are not parallel.

Since ${m}_{1} \cdot {m}_{2} \ne - 1$, they are not perpendicular.

Hence, they are neither.

I hope that this was helpful.