SOLUTION: Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line. Perpendicular to the line -4x + 5y = -23; containin

Question 388332: Find an equation for the line with the given properties. Express the answer using the general form of the equation of a line.
Perpendicular to the line -4x + 5y = -23; containing the point (-3, 7)
-3x - 5y = -23
-4x - 5 = -4
-5x + 4y = -13
-5x - 4y = -13

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Add to 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

Multiply both sides by 4

Distribute.

Add 5x to both sides.

Add 28 to both sides.

Combine like terms.

Rearrange the terms.

Note: if you multiply EVERY term of the last answer choice by -1, you'll get the last equation I've shown. So this means that the two equations are equivalent.

So the answer choice is choice D), although it's a strange way to represent an answer.

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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