SOLUTION: Consider the line y = 2x-7. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?

Algebra ->  Points-lines-and-rays -> SOLUTION: Consider the line y = 2x-7. What is the slope of a line parallel to this line? What is the slope of a line perpendicular to this line?      Log On


   

Question 1026613: Consider the line y = 2x-7.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Problem: Consider the line y = 2x-7

Question: What is the slope of a line parallel to this line?

Answer: 2

Explanation:

The slope of the given line y+=+2x-7 is m = 2 since this is in the form y+=+mx%2Bb and m is the slope. Basically it's the number to the left of the 'x'

The slope of ANY line parallel to the given line will also have a slope of 2.

Rule: Parallel lines have equal slopes

So if the given line has a slope of 2, and any line parallel to it has an equal slope, then that means any line parallel to y+=+2x-7 will have a slope of 2.

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Problem: Consider the line y = 2x-7

Question: What is the slope of a line perpendicular to this line?

Answer: -1/2

Explanation:

The slope of the given line is 2. This can be rewritten in fraction form as 2/1 since x/1 = x.

To find the perpendicular slope, you have to flip the fraction and flip the sign

flip the fraction: 2/1 ---> 1/2
flip the sign: +1/2 ----> -1/2

The original slope is 2/1. The perpendicular slope is -1/2
Notice how multiplying the two slopes yields -1
(2/1)*(-1/2) = (2*-1)/(1*2) = -2/2 = -1

Rule: (original slope)*(perpendicular slope) = -1

Note: the original slope cannot be 0