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

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) (Show Source): You can put this solution on YOUR website!
Method #1

Start with the given equation.

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

. So which means that the perpendicular equation is which in slope-intercept form is

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

Start with the given equation.

Subtract from both sides.

Rearrange the terms.

Divide both sides by to isolate y.

Break up the fraction.

Reduce.

We can see that the equation has a slope and a y-intercept .

Now to find the slope of the perpendicular line, simply flip the slope to get . Now change the sign to get . So the perpendicular slope is .

Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope and the coordinates of the given point .

Start with the point slope formula

Plug in , , and

Rewrite as

Distribute

Multiply

Subtract 2 from both sides.

Combine like terms.

So the equation of the line perpendicular to that goes through the point is . This equation is in standard form.

So the answer is either or .

Here's a graph to visually verify our answer:

Graph of the original equation (red) and the perpendicular line (green) through the point .

Answer by checkley77(12844) (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 300x300 7pixels, x from -10 to 10, y from -10 to 10, of TWO functions -x/5 +6/5 and 5x/8 -7).
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