SOLUTION: determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-4y=-5 8x+6y=-5

Algebra ->  Graphs -> SOLUTION: determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither. 3x-4y=-5 8x+6y=-5      Log On


   

Question 145400: determine whether the graphs of the equations are parallel lines, perpendicular lines, or neither.
3x-4y=-5
8x+6y=-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To figure out if one line is parallel/perpendicular to another, we must compare the two slopes of the two lines


So let's solve 3x-4y=-5 for y


3x-4y=-5 Start with the first equation


-4y=-5-3x Subtract 3+x from both sides


-4y=-3x-5 Rearrange the equation


y=%28-3x-5%29%2F%28-4%29 Divide both sides by -4


y=%28-3%2F-4%29x%2B%28-5%29%2F%28-4%29 Break up the fraction


y=%283%2F4%29x%2B5%2F4 Reduce



So the equation is now in slope-intercept form (y=mx%2Bb) where the slope is m=3%2F4 and the y-intercept is b=5%2F4



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Now let's solve 8x%2B6y=-5 for y


8x%2B6y=-5 Start with the given equation


6y=-5-8x Subtract 8+x from both sides


6y=-8x-5 Rearrange the equation


y=%28-8x-5%29%2F%286%29 Divide both sides by 6


y=%28-8%2F6%29x%2B%28-5%29%2F%286%29 Break up the fraction


y=%28-4%2F3%29x-5%2F6 Reduce



So the equation is now in slope-intercept form (y=mx%2Bb) where the slope is m=-4%2F3 and the y-intercept is b=-5%2F6



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From the two equations, we found the first slope was m=3%2F4 and the second slope was m=-4%2F3. Notice how the second slope is simply the negative reciprocal of the first slope. So this tells us that the two lines are perpendicular.



If you don't believe me, or you need more proof, here's visual proof


Graph of 3x-4y=-5 (red) and 8x%2B6y=-5 (green)