Question 162855
Note: you don't need to find the equation of the line, you only need the slopes of two lines to figure if they are parallel, perpendicular, or neither


Slope of PQ:



{{{m=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula.



{{{m=(5-1)/(6--2)}}} Plug in {{{y[2]=5}}}, {{{y[1]=1}}}, {{{x[2]=6}}}, and {{{x[1]=-2}}}. These values come from the points P(-2,1) and Q(6,5) 



{{{m=(4)/(6--2)}}} Subtract {{{1}}} from {{{5}}} to get {{{4}}}



{{{m=(4)/(8)}}} Subtract {{{-2}}} from {{{6}}} to get {{{8}}}



{{{m=1/2}}} Reduce



So the slope of the line that goes through the points P(-2,1) and Q(6,5) is {{{m=1/2}}}



Since the product of the given slope -2 and the slope {{{1/2}}} is {{{(-2)(1/2)=-2/2=-1}}}, this means that the two lines are perpendicular.



Note: you used the same slope twice to get your answer. You forgot to calculate the slope of the line that goes through PQ (see above)