SOLUTION: 2x+3y=2 Please find the slope 3x-2y=4 Please find the slope Pls advise if the lines are parallel, perpendicular or neither

Algebra ->  Coordinate-system -> SOLUTION: 2x+3y=2 Please find the slope 3x-2y=4 Please find the slope Pls advise if the lines are parallel, perpendicular or neither       Log On


   

Question 180760: 2x+3y=2 Please find the slope
3x-2y=4 Please find the slope
Pls advise if the lines are parallel, perpendicular or neither

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2B3y=2 Start with the first equation.


3y=-2x%2B2 Rearrange the terms.


y=%28-2x%2B2%29%2F%283%29 Divide both sides by 3 to isolate y.


y=%28%28-2%29%2F%283%29%29x%2B%282%29%2F%283%29 Break up the fraction.


y=-%282%2F3%29x%2B2%2F3 Reduce.


So we can see that the equation y=-%282%2F3%29x%2B2%2F3 has a slope m=-2%2F3 and a y-intercept b=2%2F3.

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3x-2y=4 Now move onto the second equation.


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


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


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


y=%283%2F2%29x-2 Reduce.


So we can see that the equation y=%283%2F2%29x-2 has a slope m=3%2F2 and a y-intercept b=-2.


So the slope of the first line is m=-2%2F3 and the slope of the second line is m=3%2F2.


Notice how the slope of the second line m=3%2F2 is simply the negative reciprocal of the slope of the first line m=-2%2F3.


In other words, if you flip the fraction of the second slope and change its sign, you'll get the first slope.


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Answer:


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