SOLUTION: write an equation perpendicular to 2x - y = 1 going through (3,5) and graph

Algebra ->  Graphs -> SOLUTION: write an equation perpendicular to 2x - y = 1 going through (3,5) and graph      Log On


   

Question 339012: write an equation perpendicular to 2x - y = 1 going through (3,5) and graph
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-y=1 Start with the given equation.


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


-y=-2x%2B1 Rearrange the terms.


y=%28-2x%2B1%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-2%29%2F%28-1%29%29x%2B%281%29%2F%28-1%29 Break up the fraction.


y=2x-1 Reduce.


We can see that the equation y=2%2Ax-1 has a slope m=2 and a y-intercept b=-1.


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=%28-1%2F2%29%28x-3%29 Plug in m=-1%2F2, x%5B1%5D=3, and y%5B1%5D=5


y-5=%28-1%2F2%29x%2B%28-1%2F2%29%28-3%29 Distribute


y-5=%28-1%2F2%29x%2B3%2F2 Multiply


y=%28-1%2F2%29x%2B3%2F2%2B5 Add 5 to both sides.


y=%28-1%2F2%29x%2B13%2F2 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 2x-y=1 that goes through the point is y=%28-1%2F2%29x%2B13%2F2.


Here's a graph to visually verify our answer:


Graph of the original equation y=2%2Ax-1 (red) and the perpendicular line y=%28-1%2F2%29x%2B13%2F2 (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