SOLUTION: Find the slope of the line being described. Graph all lines. Perpendicular to 6x-4y=16 and thru (-4,6)

Algebra ->  Linear-equations -> SOLUTION: Find the slope of the line being described. Graph all lines. Perpendicular to 6x-4y=16 and thru (-4,6)      Log On


   

Question 184600: Find the slope of the line being described. Graph all lines.
Perpendicular to 6x-4y=16 and thru (-4,6)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

6x-4y=16 Start with the given equation.


-4y=16-6x Subtract 6x from both sides.


-4y=-6x%2B16 Rearrange the terms.


y=%28-6x%2B16%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=%28%28-6%29%2F%28-4%29%29x%2B%2816%29%2F%28-4%29 Break up the fraction.


y=%283%2F2%29x-4 Reduce.


We can see that the equation y=%283%2F2%29x-4 has a slope m=3%2F2 and a y-intercept b=-4.


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-6=%28-2%2F3%29%28x--4%29 Plug in m=-2%2F3, x%5B1%5D=-4, and y%5B1%5D=6


y-6=%28-2%2F3%29%28x%2B4%29 Rewrite x--4 as x%2B4


y-6=%28-2%2F3%29x%2B%28-2%2F3%29%284%29 Distribute


y-6=%28-2%2F3%29x-8%2F3 Multiply


y=%28-2%2F3%29x-8%2F3%2B6 Add 6 to both sides.


y=%28-2%2F3%29x%2B10%2F3 Combine like terms. note: If you need help with fractions, check out this solver.


So the equation of the line perpendicular to 6x-4y=16 that goes through the point is y=%28-2%2F3%29x%2B10%2F3.


Here's a graph to visually verify our answer:
Graph of the original equation y=%283%2F2%29x-4 (red) and the perpendicular line y=%28-2%2F3%29x%2B10%2F3 (green) through the point .