SOLUTION: Find the equation of the line passing through (-1, 2) and perpendicular to y = 3x + 5.

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Question 347816: Find the equation of the line passing through (-1, 2) and perpendicular to y = 3x + 5.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
We can see that the equation y=3x%2B5 has a slope m=3 and a y-intercept b=5.


Now to find the slope of the perpendicular line, simply flip the slope m=3 to get m=1%2F3. Now change the sign to get m=-1%2F3. So the perpendicular slope is m=-1%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%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=%28-1%2F3%29%28x--1%29 Plug in m=-1%2F3, x%5B1%5D=-1, and y%5B1%5D=2


y-2=%28-1%2F3%29%28x%2B1%29 Rewrite x--1 as x%2B1


y-2=%28-1%2F3%29x%2B%28-1%2F3%29%281%29 Distribute


y-2=%28-1%2F3%29x-1%2F3 Multiply


y=%28-1%2F3%29x-1%2F3%2B2 Add 2 to both sides.


y=%28-1%2F3%29x%2B5%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to y=3x%2B5 that goes through the point is y=%28-1%2F3%29x%2B5%2F3.


Here's a graph to visually verify our answer:


Graph of the original equation y=3x%2B5 (red) and the perpendicular line y=%28-1%2F3%29x%2B5%2F3 (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