SOLUTION: graphs of equations perpendicular, parallel or neither 6x+5y=3 5x-6y=8

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Question 166670: graphs of equations perpendicular, parallel or neither
6x+5y=3
5x-6y=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x%2B5y=3 Start with the first equation.


5y=3-6x Subtract 6x from both sides.


5y=-6x%2B3 Rearrange the terms.


y=%28-6x%2B3%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28%28-6%29%2F%285%29%29x%2B%283%29%2F%285%29 Break up the fraction.


y=-%286%2F5%29x%2B3%2F5 Reduce.


So we can see that the equation y=-%286%2F5%29x%2B3%2F5 has a slope m=-6%2F5 and a y-intercept b=3%2F5.


5x-6y=8 Now move onto the second equation.


-6y=-5x%2B8 Rearrange the terms.


y=%28-5x%2B8%29%2F%28-6%29 Divide both sides by -6 to isolate y.


y=%28%28-5%29%2F%28-6%29%29x%2B%288%29%2F%28-6%29 Break up the fraction.


y=%285%2F6%29x-4%2F3 Reduce.


So we can see that the equation y=%285%2F6%29x-4%2F3 has a slope m=5%2F6 and a y-intercept b=-4%2F3.


So the slope of the first line is m=-6%2F5 and the slope of the second line is m=5%2F6.


Notice how the slope of the second line m=5%2F6 is simply the negative reciprocal of the slope of the first line m=-6%2F5.


In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope. So this means that the graphs of y=-%286%2F5%29x%2B3%2F5 and y=%285%2F6%29x-4%2F3 are perpendicular lines.


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Answer:

Consequently, this means that the graphs of 6x%2B5y=3 and 5x-6y=8 are perpendicular lines.