How do you write an equation of a line passing through (2, 6), perpendicular to 2x -3y = 12?

1 Answer
Jan 21, 2017

3x+2y=18

Explanation:

color(red)"THINGS TO REMEMBER"

color(red)(bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")

color(blue)("If a line has a slope of "m)
color(white)("XXXX")color(blue)("all lines perpendicular to it have a slope of "-1/m)

color(red)(bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")

color(white)("XX")color(blue)("A line in standard form: "Ax+BY=C)color(white)("XX")
color(white)("XXXX")color(blue)("has a slope of "-A/B)

color(red)(bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")

color(white)("XX")color(blue)("The point-slope form for a line with")
color(white)("XX")color(blue)("point "(a,b)" and slope "m" is"color(white)(*XXX"))
color(white)("XXXXXX")color(blue)(y-a=m(x-b))

color(red)(bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")

color(green)("SOLVING THE GIVEN PROBLEM")

2x-3y=12 has a slope of m=2/3

All lines perpendicular to 2x-3y=12 have a slope of -3/2

The equation of a line with slope (-3/2) through the point (2,6)
in slope-point form is:
color(white)("XXXXXX")y-6=-3/2(x-2)

color(green)("~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~")

While the above slope-point form would be a valid answer,
we would normally convert this into standard form:

y-6=-3/2(x-2)

color(white)("XXX")rarr 2y-12=-3x+6

color(white)("XXX")rarr 3x+2y=18

color(green)(bar(color(white)("XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX")