SOLUTION: Please help me solve this problem. Write an equation of the line containing the given point and perpendicular to the given line. (8,-2) 8x+5y=6 I thought that you would pl

Algebra ->  Points-lines-and-rays -> SOLUTION: Please help me solve this problem. Write an equation of the line containing the given point and perpendicular to the given line. (8,-2) 8x+5y=6 I thought that you would pl      Log On


   

Question 221112: Please help me solve this problem.
Write an equation of the line containing the given point and perpendicular to the given line.
(8,-2) 8x+5y=6
I thought that you would plug 8 in place of x and plug -2 in place of y and then solve. But I am not so sure. So confused.Please help!
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Method #1

8x%2B5y=6 Start with the given equation.

ANY equation perpendicular to the equation above will be in the form 5x-8y=c (note: just swap the coefficients and negate the second coefficient). So just plug in (8,2) to find 'c':

5%288%29-8%28-2%29=40%2B16=56. So c=56 which means that the perpendicular equation is 5x-8y=56 which in slope-intercept form is y=%285%2F8%29x-7


So you were thinking of something similar to this (actually I think you were trying to use a rule for parallel equations).


If the method above made no sense, then check out this alternative...

=========================================================
Method #2


8x%2B5y=6 Start with the given equation.


5y=6-8x Subtract 8x from both sides.


5y=-8x%2B6 Rearrange the terms.


y=%28-8x%2B6%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28%28-8%29%2F%285%29%29x%2B%286%29%2F%285%29 Break up the fraction.


y=-%288%2F5%29x%2B6%2F5 Reduce.


We can see that the equation y=-%288%2F5%29x%2B6%2F5 has a slope m=-8%2F5 and a y-intercept b=6%2F5.


Now to find the slope of the perpendicular line, simply flip the slope m=-8%2F5 to get m=-5%2F8. Now change the sign to get m=5%2F8. So the perpendicular slope is m=5%2F8.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-8%2F5 and the coordinates of the given point .


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


y--2=%285%2F8%29%28x-8%29 Plug in m=5%2F8, x%5B1%5D=8, and y%5B1%5D=-2


y%2B2=%285%2F8%29%28x-8%29 Rewrite y--2 as y%2B2


y%2B2=%285%2F8%29x%2B%285%2F8%29%28-8%29 Distribute


y%2B2=%285%2F8%29x-5 Multiply


y=%285%2F8%29x-5-2 Subtract 2 from both sides.


y=%285%2F8%29x-7 Combine like terms.


So the equation of the line perpendicular to 8x%2B5y=6 that goes through the point is y=%285%2F8%29x-7. This equation is 5x-8y=56 in standard form.


So the answer is either y=%285%2F8%29x-7 or 5x-8y=56.


Here's a graph to visually verify our answer:


Graph of the original equation y=-%288%2F5%29x%2B6%2F5 (red) and the perpendicular line y=%285%2F8%29x-7 (green) through the point .

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(8,-2)
8x+5y=6
5y=-8x+6
y=-8x/5+6/5 this line has a slope=-8/5. (red line)
Therefore any perpendicular line will have a slope=5/8.
Y=mX+b
-2=5/8*8+b
-2=40/8+b
-2=5+b
b=-2-5
b=-7 the y intercept.
y=5x/8-7 (green line).
+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C+-8x%2F5+%2B6%2F5+%2C+5x%2F8+-7%29+ (graph 300x300 7pixels, x from -10 to 10, y from -10 to 10, of TWO functions -x/5 +6/5 and 5x/8 -7).