SOLUTION: Write the equation of a line perpendicular to the line y=-2x-4 that goes through the point(-6,5)

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Question 236575: Write the equation of a line perpendicular to the line y=-2x-4 that goes through the point(-6,5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

We can see that the equation y=-2x-4 has a slope m=-2 and a y-intercept b=-4.


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


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=%281%2F2%29%28x--6%29 Plug in m=1%2F2, x%5B1%5D=-6, and y%5B1%5D=5


y-5=%281%2F2%29%28x%2B6%29 Rewrite x--6 as x%2B6


y-5=%281%2F2%29x%2B%281%2F2%29%286%29 Distribute


y-5=%281%2F2%29x%2B3 Multiply


y=%281%2F2%29x%2B3%2B5 Add 5 to both sides.


y=%281%2F2%29x%2B8 Combine like terms.


So the equation of the line perpendicular to y=-2x-4 that goes through the point is y=%281%2F2%29x%2B8.


Here's a graph to visually verify our answer:


Graph of the original equation y=-2x-4 (red) and the perpendicular line y=%281%2F2%29x%2B8 (green) through the point .