SOLUTION: Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0 Can you please show me how to figure this out? I don't

Algebra ->  Linear-equations -> SOLUTION: Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0 Can you please show me how to figure this out? I don't      Log On


   

Question 207553This question is from textbook
: Find the general form of the equation of the line that passes through (-2,-5) and is perpendicular to the graph of 3x+2y=0
Can you please show me how to figure this out? I don't even know where to begin. Thank you so very much for your help and for your time.
This question is from textbook

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

3x%2B2y=0 Start with the given equation.


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


y=%28-3x%29%2F2 Divide both sides by 2 to isolate y.


y=-%283%2F2%29x Simplify


We can see that the equation y=-%283%2F2%29x has a slope m=-3%2F2 and a y-intercept b=0.


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


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-3%2F2 and the coordinates of the given point .


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


y--5=%282%2F3%29%28x--2%29 Plug in m=2%2F3, x%5B1%5D=-2, and y%5B1%5D=-5


y--5=%282%2F3%29%28x%2B2%29 Rewrite x--2 as x%2B2


y%2B5=%282%2F3%29%28x%2B2%29 Rewrite y--5 as y%2B5


y%2B5=%282%2F3%29x%2B%282%2F3%29%282%29 Distribute


y%2B5=%282%2F3%29x%2B4%2F3 Multiply


y=%282%2F3%29x%2B4%2F3-5 Subtract 5 from both sides.


y=%282%2F3%29x-11%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 3x%2B2y=0 that goes through the point is y=%282%2F3%29x-11%2F3.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%283%2F2%29x (red) and the perpendicular line y=%282%2F3%29x-11%2F3 (green) through the point .