What is an equation for the line that is parallel to #3x - 2y = 6# and passes through #(3, -1)#?

1 Answer
Jim G.
Apr 13, 2018

#y=3/2x-11/2#

Explanation:

#"the equation of a line in "color(blue)"slope-intercept-form"# is.

#•color(white)(x)y=mx+b#

#"where m is the slope and b the y-intercept"#

#"rearrange "3x-2y=6" into this form"#

#"subtract 3x from both sides"#

#cancel(3x)cancel(-3x)-2y=-3x+6#

#rArr-2y=-3x+6#

#"divide all terms by "-2#

#rArry=3/2x-3larrcolor(blue)"in slope-intercept form"#

#"with slope m "=3/2#

#• " Parallel lines have equal slopes"#

#rArry=3/2x+blarrcolor(blue)"is the partial equation"#

#"to find b substitute "(3,-1)" into the partial equation"#

#-1=9/2+brArrb=-1-9/2=-11/2#

#rArry=3/2x-11/2larrcolor(red)"equation of parallel line"#

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