SOLUTION: This is a summer Assignment. I don't have a book. "Write the equation of the line perpendicular to the line y=1/2x + 2 that passes through the point (-4,5)."

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: This is a summer Assignment. I don't have a book. "Write the equation of the line perpendicular to the line y=1/2x + 2 that passes through the point (-4,5)."      Log On


   

Question 150985: This is a summer Assignment. I don't have a book.
"Write the equation of the line perpendicular to the line y=1/2x + 2 that passes through the point (-4,5)."
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!



We can see that the equation y=%281%2F2%29x%2B2 has a slope m=1%2F2 and a y-intercept b=2.


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-5=-2%28x--4%29 Plug in m=-2, x%5B1%5D=-4, and y%5B1%5D=5


y-5=-2%28x%2B4%29 Rewrite x--4 as x%2B4


y-5=-2x%2B-2%284%29 Distribute


y-5=-2x-8 Multiply


y=-2x-8%2B5 Add 5 to both sides.


y=-2x-3 Combine like terms.


So the equation of the line perpendicular to y=%281%2F2%29x+%2B+2 that goes through the point is y=-2x-3.


Here's a graph to visually verify our answer:
Graph of the original equation y=%281%2F2%29x%2B2 (red) and the perpendicular line y=-2x-3 (green) through the point .