Question 120587
Step 1:  Find the equation of the line through (0,5) and (-3,-4).  Use the two-point form of the line because you are given two points.


{{{y-y[1]=((y[2]-y[1])/(x[2]-x[1]))(x-x[1])}}}


It doesn't matter which point you call 1 and which you call 2 as long as you are consistent.  Let's say (0,5) is point 1, ({{{x[1]}}},{{{y[1]}}}).


Then the equation for the line becomes:


{{{y-5=(((-4)-5)/(-3-0))(x-0)}}}


And then a little arithmetic to get:


{{{y-5=((-9)/(-3))x}}}
{{{y-5=3x}}}


And then put the equation into slope-intercept form by solving for y,


{{{y=3x+5}}}


Now, by inspection of the coefficient on the x term, we can see that the slope of the line through the points is 3.


But we want the slope of a perpendicular line.  The rule is that line {{{L[1]}}} is perpendicular to line {{{L[2]}}} if and only if slope {{{m[1]}}} is the negative reciprocal of slope {{{m[2]}}}, that is: {{{m[1]=-1/m[2]}}}


All we need now is the negative reciprocal of 3, namely {{{-1/3}}}