Question

Are these two lines parallel, perpendicular, the same line, or none of these?−3x=3y+64x+4y=2O a) perpendicularO b) the same lineO c) parallelO d) none of these

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asked 2021-06-16

Are these two lines parallel, perpendicular, the same line, or none of these?

\(−3x=3y+6\)
\(4x+4y=2\)
a) perpendicular
b) the same line
c) parallel
d) none of these

Answers (1)

2021-06-17

Two lines are parallel if their slopes are the same (or equal). Two lines are perpendicular if their slopes are negative reciprocals.
Write each line in slope-intercept form \(y=mx+b\) by solving for y.
\(\displaystyle−{3}{x}−{3}{y}+{6}→{y}=−{x}−{2}\)
\(\displaystyle{4}{x}+{4}{y}={2}→{y}=−{x}+\frac{{1}}{{2}}\)
Since both lines have a slope of −1, then they are c) parallel.

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