Question 114529
Find the slope of the line that is perpendicular to {{{3x+2y=4}}}


Perpendicular lines and their slopes: {{{m[1] = -1/m[2]}}} 

In other words, perpendicular slopes are {{{negative}}}{{{ reciprocals }}}of each other.


{{{3x+2y=4}}}….first we need to write this equation in {{{slope_intercept}}} form {{{y = mx + b}}} like this:

{{{2y= -3x + 4}}}…….divide both sides by {{{2}}}

{{{2y/2 = -3x/2 + 4/2}}}…….

{{{y = -(3/2)x + 2}}}……….this is {{{slope_intercept}}} form, and we see that {{{m[1] =-3/2}}} and {{{b=2}}}
	
{{{m[1] = -3/2}}}

Now find {{{m[2]}}}

{{{m[1] = -1/m[2]}}}............substitute {{{m[1]}}} with {{{ -3/2}}}

{{{-3/2 = -1/m[2]}}}………….multiply both sides by {{{ m[2] }}}


{{{-(3/2) m[2]  = -(1/m[2]) m[2] }}}………….

{{{-(3/2) m[2]  = -1 }}}………….divide bothe sides by {{{ -3/2 }}}

{{{-(3/2) m[2]/ (-3/2)   = (-1)/(-3/2)  }}}………….
	
{{{m[2] = (-1)/(-3/2)  }}}………….....we can write {{{-1}}} as {{{-1/1}}}

{{{m[2] = (-1/1)/(-3/2)  }}}………….simplify

{{{m[2] = (-2)/-3}}}………….

{{{m[2] = 2/3}}}…………....your solution