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+
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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) (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 , a line perpendicular to that is .
2) To find the slope of a line, you follow this formula:
______________
(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)
__________
, which is:
__________
which is:
= 1 or
What is the negative reciprocal of ?
The negative reciprocal is: 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 and refer to a point that the line goes thru. Here is the point slope equation of a line:
Now just fill in with this info:
m = -1
(point slope equation of line)
(fill in given values, which computes to...)
(<---which computes to this line)
(distribute the -1 to the "x" and to the 4)
(subtract -10 from both sides)
(final answer)
Therefore, your answer is "b" which is: b. Y= -x-14
I hope this helps you! :-)
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