Question 189828
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
Given Line ---> 2x + 3y =4


Remember Slope-Intercept Form, {{{y=mx+b}}}, where{{{system(m=Slope,b=yIntercept)}}}


Going back to our Line Eqn and transforming it to our Slope-Intercept Form:


Isolate "y" by moving "x" to the right: (change sign, + or -)


{{{3y=-2x+4}}}, divide "3" the left & right terms:
{{{cross(3)y/cross(3)=(-2x+4)/3=(-2/3)x+4/3}}}
{{{red(y=(-2/3)x+4/3)}}}


As per our Slope-Intercept Form, we find <font color=blue>Slope=m=-2/3</font>


Now, the line perpendicular to 2x+3y=4 has a {{{Slope=m[2]=-1/m}}}, negative reciprocal.
So, {{{Slope=m[2]=-1/(-2/3)=(-1)(-3/2)=highlight(3/2)}}}, Answer


Thank you,
Jojo</font>