004 Sample Final A, Problem 14

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a) Find an equation of the line passing through (-4, 2) and (3, 6).
b) Find the slope of any line perpendicular to your answer from a)

Foundations
1) How do you find the slope of a line through points and ?
2) What is the equation of a line?
3) How do you find the slope of a line perpendicular to a line ?
Answer:
1) The slope is given by .
2) The equation of a line is where is a point on the line.
3) The slope is given by where is the slope of the line .


Solution:

Step 1:
Using the above equation, the slope is equal to .
Step 2:
The equation of the line is . Solving for ,
we get .
Step 3:
The slope of any line perpendicular to the line in Step 2 is .
Final Answer:
The slope is , the equation of the line is , and
the slope of any line perpendicular to this line is .

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