SOLUTION: The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is? a. Y= x+9 b. Y= -x-14 c. Y= -x+

Algebra ->  Linear-equations -> SOLUTION: The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is? a. Y= x+9 b. Y= -x-14 c. Y= -x+      Log On


   

Question 202834: The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is?
a. Y= x+9
b. Y= -x-14
c. Y= -x+9
d. Y= 16x+54
Answer by PRMath(133) About Me  (Show Source):
You can put this solution on YOUR website!
The equation of the line that contains the point (-4, -10) and is perpendicular to the line that contains the points (-3, 6)and (3, 12) is?
a. Y= x+9
b. Y= -x-14
c. Y= -x+9
d. Y= 16x+54
Ok, let's start this from the idea that the equation of the line must be perpendicular to the points (-3, 6)and (3, 12). There are two facts you must know to solve this problem:

1) Perpendicular lines have slopes that are NEGATIVE reciprocals of one another. That's just a fancy way of saying you "flip" them and take the opposite. Sooo, if your slope is 3%2F4, a line perpendicular to that is -3%2F4.


2) To find the slope of a line, you follow this formula:

y%5B2%5D-y%5B1%5D
______________
x%5B2%5D-x%5B1%5D
(I am very sorry this fraction does not look nice. I am not adept yet at making fractions and what-not on this site).


So, let's find the slope of these ordered pairs:

(-3, 6)and (3, 12)

12-6
__________
3-+-3, which is:

12-6
__________
3%2B3 which is:

6%2F6 = 1 or 1%2F1


What is the negative reciprocal of 1%2F1?
The negative reciprocal is: -1%2F1 or: -1


Now we must make sure that the equation of the line includes the point (-4, -10) and must have a slope of -1 if it is to be perpendicular to the line that contains the points (-3, 6)and (3, 12).

To find this equation of a line, you would need the POINT SLOPE equation of a line. In other words, you know a point on the line (-4, -10) and you know the slope is -1 sooo, you just fill that info into the point slope equation of a line.

Let's look at the POINT SLOPE equation of a line. In this equation, "m" is the slope and y%5B1%5D and x%5B1%5D refer to a point that the line goes thru. Here is the point slope equation of a line:

y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29

Now just fill in with this info:
m = -1
x%5B1%5D+=+-4
y%5B1%5D+=+-10

y-y%5B1%5D+=+m%28x+-+x%5B1%5D%29 (point slope equation of line)
y+-++-10+=+-1%28x+-+-4%29 (fill in given values, which computes to...)
y+%2B10+=+-1%28x%2B4%29 (<---which computes to this line)
y+%2B10+=+-1x+-+4 (distribute the -1 to the "x" and to the 4)
y+=+-1x+-+4+-10 (subtract -10 from both sides)
y+=+-1x+-14 (final answer)

Therefore, your answer is "b" which is: b. Y= -x-14
I hope this helps you! :-)