SOLUTION: I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated. The following is the pro

Question 376122: I have been trying for hours to solve the following type of equations and get stuck toward the end. Any help you can provide would be greatly appreciated. The following is the problem and below is what I am trying:
Write an equation of the line containing the given point and perpendicular to the given line
(9, -4); 6x + 5y = 4
ME: 5y=-6x+4
y= 6/5x+4/5
y-(-4)=6/5(x-9)
I believe I have to subtract 4 from each side but this is where I keep getting confused. Thanks in advance for any help
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

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 . Recall that subtracting a negative is the same as adding a positive.

Distribute

Multiply

Subtract 4 from both sides.

Combine like terms. note: If you need help with fractions, check out this solver.

So the equation of the line perpendicular to that goes through the point

is .

Here's a graph to visually verify our answer:

Graph of the original equation (red) and the perpendicular line (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
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