SOLUTION: Determine whether the pair of lines is parallel, perpendicular, or neither. X-3y= -2 Y= 4X - 3

Algebra ->  Linear-equations -> SOLUTION: Determine whether the pair of lines is parallel, perpendicular, or neither. X-3y= -2 Y= 4X - 3      Log On


   

Question 1049115: Determine whether the pair of lines is parallel, perpendicular, or neither.
X-3y= -2
Y= 4X - 3
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +x+-+3y+=+-2+
(2) +y+=+4x+-+3+
------------------
Put both equations into the
slope-intercept form which
will look like:
+y+=+m%2Ax+%2B+b+ where
+m+ = slope
+b+ = y-intercept
---------------------------
Subtract +x+ from both sides of (1)
(1) +-3y+=+-x+-+2+
Divide both sides by +-3+
(1) +y+=+-x%2F%28-3%29+-+2%2F%28-3%29+
Note that (-)/(-) = (+) ,so
(1) +y+=+%281%2F3%29%2Ax+%2B+2%2F3+
-----------------------------
Note that (2) is already in the slope-intercept form
(2) +y+=+4x+-+3+
-----------------------
If these lines were parallel, then their slopes would
be the same, and they are not
If these lines were perpendicular, then their slopes
would have the relation:
+m%5B1%5D+=+-1%2Fm%5B2%5D+
If +m%5B1%5D+=+1%2F3+, solve for +m%5B2%5D+
+1%2F3+=+-1%2Fm%5B2%5D+
+m%5B2%5D+=+-3+
But actually, +m%5B2%5D+=+4+, so these
line are neither parallel nor perpendicular