SOLUTION: Find an equation for the line containing the point (-2,6) and perpendicular to the line 2x + y = 5.

Algebra ->  Linear-equations -> SOLUTION: Find an equation for the line containing the point (-2,6) and perpendicular to the line 2x + y = 5.       Log On


   

Question 195754: Find an equation for the line containing the point (-2,6) and perpendicular to the line 2x + y = 5.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x%2By=5 Start with the given equation.


y=5-2x Subtract 2x from both sides.


y=-2x%2B5 Rearrange the terms.


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


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=-2 and the coordinates of the given point .


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


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


y-6=%281%2F2%29%28x%2B2%29 Rewrite x--2 as x%2B2


y-6=%281%2F2%29x%2B%281%2F2%29%282%29 Distribute


y-6=%281%2F2%29x%2B1 Multiply


y=%281%2F2%29x%2B1%2B6 Add 6 to both sides.


y=%281%2F2%29x%2B7 Combine like terms.


So the equation of the line perpendicular to 2x%2By=5 that goes through the point is y=%281%2F2%29x%2B7.


Here's a graph to visually verify our answer:



Graph of the original equation y=-2%2Ax%2B5 (red) and the perpendicular line y=%281%2F2%29x%2B7 (green) through the point .