Find the slope of a line perpendicular to each given line ?

Question

y=3 over 2 x-4 

Answer 1

As you have written it, I will assume that your equation reads....

 

y=(3/2)x-4.........given equation Eq1, problem statement

 

Recognize that this equation is already in "slope-intercept" form 

(y=mx+b), slope is "m" and the y-intercept is "(0,b)."

 

So the slope and y-intercept of Eq1 is...

m=3/2

y-intercept=(0,-4)

 

The slope of a perpendicular line to Eq1 "m_⊥" is the "negative

inverse" of the slope "m" of Eq1.  So....

m_⊥=-(1/m)

     =-(1/(3/2))

     =-2/3