Question 106451
In order to find a perpendicular line, you first need to find the slope of the original line and then find the negative reciprocal.


{{{3x-2y=-1}}}


needs to be put into {{{y = mx+b}}} form.


{{{-2y=-3x-1}}}
{{{y=3x/2+1}}}


Hence, the slope of the line is {{{3/2}}} and the slope of any perpendicular line would be {{{-2/3}}}


also, since y is a function of x in this case, the equation in function notation would be {{{f(x)=3x/2+1}}}


Since you are given a point to further define your perpendicular, you need to use the point-slope form of a line, given by:


{{{y-y1=m(x-x1)}}} 


Substituting:


{{{y-(-7)=(-2/3)(x-2)}}}


And rearranging into slope-intercept form:


{{{y=-2x/3-17/3}}}


or in function notation,


{{{f(x)=-2x/3-17/3}}}


EXTRA CREDIT:  Graph these two lines and verify visually that they are perpendicular.