Question 154332



{{{6x-7y=5}}} Start with the given equation.



{{{-7y=5-6x}}} Subtract {{{6x}}} from both sides.



{{{-7y=-6x+5}}} Rearrange the terms.



{{{y=(-6x+5)/(-7)}}} Divide both sides by {{{-7}}} to isolate y.



{{{y=((-6)/(-7))x+(5)/(-7)}}} Break up the fraction.



{{{y=(6/7)x-5/7}}} Reduce.



So we can see that the equation {{{y=(6/7)x-5/7}}} has a slope {{{m=6/7}}} and a y-intercept {{{b=-5/7}}}.



{{{6y-7x=5}}} Now move onto the second equation.



{{{6y=57x}}} Add {{{7x}}} to both sides.



{{{6y=7x+5}}} Rearrange the terms.



{{{y=(7x+5)/(6)}}} Divide both sides by {{{6}}} to isolate y.



{{{y=((7)/(6))x+(5)/(6)}}} Break up the fraction.



{{{y=(7/6)x+5/6}}} Reduce.



So we can see that the equation {{{y=(7/6)x+5/6}}} has a slope {{{m=7/6}}} and a y-intercept {{{b=5/6}}}.



So the slope of the first line is {{{m=6/7}}} and the slope of the second line is {{{m=7/6}}}.



Since the two slopes are neither equal nor negative reciprocals of one another, the two lines are neither parallel nor perpendicular.