SOLUTION: please help..... find an equation of a line perpendicular to y=3/2x+5 and contains the point(0,0) please show me step by step thank you april

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Question 352953: please help.....
find an equation of a line perpendicular to y=3/2x+5 and contains the point(0,0)
please show me step by step
thank you
april
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=%283%2F2%29x%2B5 has a slope m=3%2F2 and a y-intercept b=5.


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=-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-0=%28-2%2F3%29%28x-0%29 Plug in m=-2%2F3, x%5B1%5D=0, and y%5B1%5D=0


y-0=%28-2%2F3%29x%2B%28-2%2F3%29%280%29 Distribute


y-0=%28-2%2F3%29x%2B0 Multiply


y=%28-2%2F3%29x Simplify (ie remove unneeded zeros).


So the equation of the line perpendicular to y=3%2F2x%2B5 that goes through the point is y=%28-2%2F3%29x.


Here's a graph to visually verify our answer:


Graph of the original equation y=%283%2F2%29x%2B5 (red) and the perpendicular line y=%28-2%2F3%29x (green) through the point .


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim