# 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

**The slope of the line**

**The slope of the line perpendicular to**

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"#