How do you find the equation of a line perpendicular to 2x+3y=9 and passing through (3,-3)?
2 Answers
Explanation:
We know that,
the slope of the line
is
Hence,the equn.of line passing through
Note:
The equn.of line passing through
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=9" into this form"
rArr3y=-2x+9
rArry=-2/3x+3larrcolor(blue)"in slope-intercept form"
"with slope m "=-2/3
"Given a line with slope then the slope of a line"
"perpendicular to it is"
•color(white)(x)m_(color(red)"perpendicular")=-1/m
rArrm_("perpendicular")=-1/(-2/3)=3/2
rArry=3/2x+blarrcolor(blue)"is the partial equation"
"to find b substitute "(3,-3)" into the partial equation"
-3=9/2+brArrb=-6/2-9/2=-15/2
rArry=3/2x-15/2larrcolor(red)"equation of perpendicular line"