SOLUTION: What is the equation of the line that passes through the given points and is perpendicular to the given line? (3,3), 2y=3x-6

Algebra ->  Linear-equations -> SOLUTION: What is the equation of the line that passes through the given points and is perpendicular to the given line? (3,3), 2y=3x-6      Log On


   

Question 174179: What is the equation of the line that passes through the given points and is perpendicular to the given line?
(3,3), 2y=3x-6
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2y=3x-6 Start with the given equation.


y=%283x-6%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%28%283%29%2F%282%29%29x%2B%28-6%29%2F%282%29 Break up the fraction.


y=%283%2F2%29x-3 Reduce.


We can see that the equation y=%283%2F2%29x-3 has a slope m=3%2F2 and a y-intercept b=-3.


Now to find the slope of the perpendicular line, simply flip the slope m=3%2F2 to get m=2%2F3. Now change the sign to get m=-2%2F3. So the perpendicular slope is m=-2%2F3.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=3%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-3=%28-2%2F3%29%28x-3%29 Plug in m=-2%2F3, x%5B1%5D=3, and y%5B1%5D=3


y-3=%28-2%2F3%29x%2B%28-2%2F3%29%28-3%29 Distribute


y-3=%28-2%2F3%29x%2B2 Multiply


y=%28-2%2F3%29x%2B2%2B3 Add 3 to both sides.


y=%28-2%2F3%29x%2B5 Combine like terms.


So the equation of the line perpendicular to -3x%2B2y=-6 that goes through the point is y=%28-2%2F3%29x%2B5.


Here's a graph to visually verify our answer:
Graph of the original equation y=%283%2F2%29x-3 (red) and the perpendicular line y=%28-2%2F3%29x%2B5 (green) through the point .