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

Algebra ->  Graphs -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
-4x%2B5y=-23 Start with the given equation.


5y=-23--4x Add 4x to both sides.


5y=--4x-23 Rearrange the terms.


y=%28--4x-23%29%2F%285%29 Divide both sides by 5 to isolate y.


y=%28%28--4%29%2F%285%29%29x%2B%28-23%29%2F%285%29 Break up the fraction.


y=%284%2F5%29x-23%2F5 Reduce.


We can see that the equation y=%284%2F5%29x-23%2F5 has a slope m=4%2F5 and a y-intercept b=-23%2F5.


Now to find the slope of the perpendicular line, simply flip the slope m=4%2F5 to get m=5%2F4. Now change the sign to get m=-5%2F4. So the perpendicular slope is m=-5%2F4.


Now let's use the point slope formula to find the equation of the perpendicular line by plugging in the slope m=-5%2F4 and the coordinates of the given point .


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


y-7=%28-5%2F4%29%28x--3%29 Plug in m=-5%2F4, x%5B1%5D=-3, and y%5B1%5D=7


y-7=%28-5%2F4%29%28x%2B3%29 Rewrite x--3 as x%2B3


4%28y-7%29=-5%28x%2B3%29 Multiply both sides by 4


4y-28=-5x-15 Distribute.


4y-28%2B5x=-15 Add 5x to both sides.


4y%2B5x=-15%2B28 Add 28 to both sides.


4y%2B5x=13 Combine like terms.


5x%2B4y=13 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