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

1 Answer
Jim G.
Jun 15, 2018

#2x+3y=5#

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 "2x+3y=6" into this form"#

#"subtract "2x" from both sides and divide all terms by 3"#

#3y=-2x+6#

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

#"with slope " =-2/3#

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

#"to find b substitute "(-2,3)" into the partial equation"#

#3=4/3+brArrb=9/3-4/3=5/3#

#y=-2/3x+5/3larrcolor(red)"in slope-intercept form"#

#"multiply through by 3"#

#3y=-2x+5#

#2x+3y=5larrcolor(red)"in standard form"#

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