SOLUTION: True or false: The lines 8x - 5y = 9 and 5x + 8y = 5 are perpendicular. Please show work...

Algebra ->  Graphs -> SOLUTION: True or false: The lines 8x - 5y = 9 and 5x + 8y = 5 are perpendicular. Please show work...      Log On


   

Question 171419: True or false: The lines 8x - 5y = 9 and 5x + 8y = 5 are perpendicular. Please show work...
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

8x-5y=9 Start with the first equation.


-5y=9-8x Subtract 8x from both sides.


-5y=-8x%2B9 Rearrange the terms.


y=%28-8x%2B9%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=%28%28-8%29%2F%28-5%29%29x%2B%289%29%2F%28-5%29 Break up the fraction.


y=%288%2F5%29x-9%2F5 Reduce.


So we can see that the equation y=%288%2F5%29x-9%2F5 has a slope m=8%2F5 and a y-intercept b=-9%2F5.

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5x%2B8y=5 Now move onto the second equation.


8y=5-5x Subtract 5x from both sides.


8y=-5x%2B5 Rearrange the terms.


y=%28-5x%2B5%29%2F%288%29 Divide both sides by 8 to isolate y.


y=%28%28-5%29%2F%288%29%29x%2B%285%29%2F%288%29 Break up the fraction.


y=-%285%2F8%29x%2B5%2F8 Reduce.


So we can see that the equation y=-%285%2F8%29x%2B5%2F8 has a slope m=-5%2F8 and a y-intercept b=5%2F8.


So the slope of the first line is m=8%2F5 and the slope of the second line is m=-5%2F8.


Notice how the slope of the second line m=-5%2F8 is simply the negative reciprocal of the slope of the first line m=8%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 y=%288%2F5%29x-9%2F5 and y=-%285%2F8%29x%2B5%2F8 are perpendicular lines.