SOLUTION: What is the equation of the line that passes through the given point and is perpendicular to the given line? (8,-1), 4y + 2x = 12 i got y= -2x-3. I tried my best, but

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: What is the equation of the line that passes through the given point and is perpendicular to the given line? (8,-1), 4y + 2x = 12 i got y= -2x-3. I tried my best, but      Log On


   

Question 174200: What is the equation of the line that passes through the given point and is perpendicular to the given line?
(8,-1), 4y + 2x = 12

i got y= -2x-3.
I tried my best, but didn't quite understand the problem, so it would be great if you could check my answer. Thankyou so much!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4y+%2B+2x+=+12 Start with the given equation.


4y=12-2x Subtract 2x from both sides.


4y=-2x%2B12 Rearrange the terms.


y=%28-2x%2B12%29%2F%284%29 Divide both sides by 4 to isolate y.


y=%28%28-2%29%2F%284%29%29x%2B%2812%29%2F%284%29 Break up the fraction.


y=-%281%2F2%29x%2B3 Reduce.


We can see that the equation y=-%281%2F2%29x%2B3 has a slope m=-1%2F2 and a y-intercept b=3.


Now to find the slope of the perpendicular line, simply flip the slope m=-1%2F2 to get m=-2%2F1. Now change the sign to get m=2. So the perpendicular slope is m=2.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-1%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--1=2%28x-8%29 Plug in m=2, x%5B1%5D=8, and y%5B1%5D=-1


y%2B1=2%28x-8%29 Rewrite y--1 as y%2B1


y%2B1=2x%2B2%28-8%29 Distribute


y%2B1=2x-16 Multiply


y=2x-16-1 Subtract 1 from both sides.


y=2x-17 Combine like terms.


So the equation of the line perpendicular to 2x%2B4y=+12 that goes through the point is y=2x-17.


Here's a graph to visually verify our answer:
Graph of the original equation y=-%281%2F2%29x%2B3 (red) and the perpendicular line y=2x-17 (green) through the point .