# What is the equation of the line perpendicular to #y=-3/2x # that passes through # (2,-4) #?

##### 1 Answer

#### Explanation:

The slope-intercept form of a line is written in the form:

#y=mx+b#

where:

Start by finding the slope that is perpendicular to

We can find the slope of the line perpendicular to **negative reciprocal**. Recall that the reciprocal of any number is

#-(1/"slope")#

#=-(1/(-3/2x))#

#=-(1-:-3/2x)#

#=-(1*-2/3x)#

#=-(-2/3x)#

#=2/3xrArr# negative reciprocal, perpendicular to#-3/2x#

So far, our equation is:

Since we do not know the value of

#y=mx+b#

#-4=2/3(2)+b#

#-4=4/3+b#

#-16/3=b#

Now that you know all your values, rewrite the equation in slope-intercept form:

#y=2/3x-16/3#