Question 1049115
(1) {{{ x - 3y = -2 }}}
(2) {{{ y = 4x - 3 }}}
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Put both equations into the 
slope-intercept form which
will look like:
{{{ y = m*x + b }}} where
{{{ m }}} = slope
{{{ b }}} = y-intercept
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Subtract {{{ x }}} from both sides of (1)
(1) {{{ -3y = -x - 2 }}}
Divide both sides by {{{ -3 }}}
(1) {{{ y = -x/(-3) - 2/(-3) }}}
Note that (-)/(-) = (+) ,so
(1) {{{ y = (1/3)*x + 2/3 }}}
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Note that (2) is already in the slope-intercept form
(2) {{{ y = 4x - 3 }}}
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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[1] = -1/m[2] }}}
If {{{ m[1] = 1/3 }}}, solve for {{{ m[2] }}}
{{{ 1/3 = -1/m[2] }}}
{{{ m[2] = -3 }}}
But actually, {{{ m[2] = 4 }}}, so these
line are neither parallel nor perpendicular