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

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Answer 1 · 2014-11-05T17:04:51

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

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

by subtracting #3x#,

#=> 5y=-3x+1#

by dividing by #5#,

#=> y=-3/5x+1/5#

So, the slope is #m_1=-3/5#.

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

by subtracting #10x#,

#=>y=-10x-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.