SOLUTION: Decide whether the pair of lines is parallel, perpendicular, or neither. 4x+3y=5 3x-4y=4 What is the slope of 4x+3y=5 What is the slope of 3x-4y=4

Algebra ->  Linear-equations -> SOLUTION: Decide whether the pair of lines is parallel, perpendicular, or neither. 4x+3y=5 3x-4y=4 What is the slope of 4x+3y=5 What is the slope of 3x-4y=4       Log On


   

Question 189713: Decide whether the pair of lines is parallel, perpendicular, or neither.
4x+3y=5
3x-4y=4
What is the slope of 4x+3y=5
What is the slope of 3x-4y=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
4x%2B3y=5 Start with the first equation.


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


3y=-4x%2B5 Rearrange the terms.


y=%28-4x%2B5%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%28-4%29%2F%283%29%29x%2B%285%29%2F%283%29 Break up the fraction.


y=-%284%2F3%29x%2B5%2F3 Reduce.


So we can see that the equation y=-%284%2F3%29x%2B5%2F3 has a slope m=-4%2F3 and a y-intercept b=5%2F3.


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3x-4y=4 Now move onto the second equation.


-4y=4-3x Subtract 3x from both sides.


-4y=-3x%2B4 Rearrange the terms.


y=%28-3x%2B4%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%28-3%29%2F%28-4%29%29x%2B%284%29%2F%28-4%29 Break up the fraction.


y=%283%2F4%29x-1 Reduce.


So we can see that the equation y=%283%2F4%29x-1 has a slope m=3%2F4 and a y-intercept b=-1.


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So the slope of the first line is m=-4%2F3 and the slope of the second line is m=3%2F4.


Notice how the slope of the second line m=3%2F4 is simply the negative reciprocal of the slope of the first line m=-4%2F3.


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=-%284%2F3%29x%2B5%2F3 and y=%283%2F4%29x-1 are perpendicular lines.


So consequently, this also means that 4x%2B3y=5 and 3x-4y=4 are perpendicular lines.