# How do you write an equation of a line perpendicular to #y=-1/2x+2/3# and passes through (2,3)?

##### 2 Answers

#### 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"#

#y=-1/2x+2/3" is in this form"#

#"with slope m "=-1/2#

#"Given a line with slope m then the slope of a line"#

#"perpendicular to it is "#

#•color(white)(x)m_(color(red)"perpendicular")=-1/m#

#rArrm_("perpendicular")=-1/(-1/2)=2#

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

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

#3=4+brArrb=3-4=-1#

#rArry=2x-1larrcolor(red)"equation of perpendicular line"#

See below

#### Explanation:

If

We know then that

Then, our perpendicular line is

However

The perpendicular line requested passing thru