SOLUTION: Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3,-2). Write the equation in standard form, with all integer coefficients.

Algebra ->  Linear-equations -> SOLUTION: Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3,-2). Write the equation in standard form, with all integer coefficients.      Log On


   

Question 183043: Find the equation, in standard form, of the line perpendicular to 2x - 3y = -5 and passing through (3,-2). Write the equation in standard form, with all integer coefficients.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x+-+3y+=+-5 Start with the given equation.


-3y=-5-2x Subtract 2x from both sides.


-3y=-2x-5 Rearrange the terms.


y=%28-2x-5%29%2F%28-3%29 Divide both sides by -3 to isolate y.


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


y=%282%2F3%29x%2B5%2F3 Reduce.


We can see that the equation y=%282%2F3%29x%2B5%2F3 has a slope m=2%2F3 and a y-intercept b=5%2F3.


Now to find the slope of the perpendicular line, simply flip the slope m=2%2F3 to get m=3%2F2. Now change the sign to get m=-3%2F2. So the perpendicular slope is m=-3%2F2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=2%2F3 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y--2=%28-3%2F2%29%28x-3%29 Plug in m=-3%2F2, x%5B1%5D=3, and y%5B1%5D=-2


y%2B2=%28-3%2F2%29%28x-3%29 Rewrite y--2 as y%2B2


2%28y%2B2%29=-3%28x-3%29 Multiply both sides by 2.


2y%2B4=-3x%2B9 Distribute


3x%2B2y%2B4=9 Add 3x to both sides.


3x%2B2y=9-4 Subtract 4 from both sides.


3x%2B2y=5 Combine like terms.


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Answer:


So the equation of the line perpendicular to 2x+-+3y+=+-5 that goes through the point in standard form is 3x%2B2y=5.


So the answer you're looking for is: 3x%2B2y=5


Here's a graph to visually verify our answer:
Graph of the original equation 2x+-+3y+=+-5 (red) and the perpendicular line 3x%2B2y=5 (green) through the point .