008A Sample Final A, Question 15

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Question: a) Find the equation of the line passing through (3, -2) and (5, 6).
                  b) Find the slope of any line perpendicular to your answer from a)

Foundations
1) We have two points on a line. How do we find the slope?
2) How do you write the equation of a line, given a point on the line and the slope?
3) For part b) how are the slope of a line and the slope of all perpendicular lines related?
Answer:
1) The formula for the slope of a line through two points and is .
2) The point-slope form of a line is where the slope of the line is m, and is a point on the line.
3) If m is the slope of a line. The slope of all perpendicular lines is

Solution:

Step 1:
Since the slope of a line passing through two points is , the slope of the line is
Final Answer part a):
Now that we have the slope of the line and a point on the line the equation for the line is . Another answer is . These answers are the same. They just look different.
Final Answer part b):
Since the slope of the line in part a) is 4, the slope of any line perpendicular to the answer in a) is

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