SOLUTION: Determine whether the lines of the graph are perpendicular. 6x-7y=5 6y-7x=5

Algebra ->  Graphs -> SOLUTION: Determine whether the lines of the graph are perpendicular. 6x-7y=5 6y-7x=5      Log On


   

Question 154332: Determine whether the lines of the graph are perpendicular.
6x-7y=5
6y-7x=5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!


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


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


-7y=-6x%2B5 Rearrange the terms.


y=%28-6x%2B5%29%2F%28-7%29 Divide both sides by -7 to isolate y.


y=%28%28-6%29%2F%28-7%29%29x%2B%285%29%2F%28-7%29 Break up the fraction.


y=%286%2F7%29x-5%2F7 Reduce.


So we can see that the equation y=%286%2F7%29x-5%2F7 has a slope m=6%2F7 and a y-intercept b=-5%2F7.


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


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


6y=7x%2B5 Rearrange the terms.


y=%287x%2B5%29%2F%286%29 Divide both sides by 6 to isolate y.


y=%28%287%29%2F%286%29%29x%2B%285%29%2F%286%29 Break up the fraction.


y=%287%2F6%29x%2B5%2F6 Reduce.


So we can see that the equation y=%287%2F6%29x%2B5%2F6 has a slope m=7%2F6 and a y-intercept b=5%2F6.


So the slope of the first line is m=6%2F7 and the slope of the second line is m=7%2F6.


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