Difference between revisions of "008A Sample Final A, Question 15"

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(Created page with "'''Question: ''' a) Find the equation of the line passing through (3, -2) and (5, 6).<br>               ...")
 
 
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!Foundations
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!Foundations: &nbsp;
 
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|1) We have two points on a line. How do we find the slope?
 
|1) We have two points on a line. How do we find the slope?
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|Answer:
 
|Answer:
 
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|1) The formula for the slope of a line through two points <math> (x_1, y_1)</math> and <math> (x_2, y_2)</math> is <math> \frac{y_2 - y_1}{x_2 - x_1}</math>.
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|1) The formula for the slope of a line through two points <math> (x_1, y_1)</math>&nbsp; and &nbsp;<math> (x_2, y_2)</math> &nbsp; is &nbsp;<math> \frac{y_2 - y_1}{x_2 - x_1}</math>.
 
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|2) The point-slope form of a line is <math> y - y_1 = m (x - x_1)</math> where the slope of the line is m, and <math>(x_1, y_1)</math> is a point on the line.
 
|2) The point-slope form of a line is <math> y - y_1 = m (x - x_1)</math> where the slope of the line is m, and <math>(x_1, y_1)</math> is a point on the line.
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! Step 1:
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!Step 1: &nbsp;
 
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|Since the slope of a line passing through two points is <math> \frac{y_2 - y_1}{x_2 - x_1} </math>, the slope of the line is <math> \frac{6 - (-2)}{5 - 3} = \frac{8}{2} = 4 </math>
 
|Since the slope of a line passing through two points is <math> \frac{y_2 - y_1}{x_2 - x_1} </math>, the slope of the line is <math> \frac{6 - (-2)}{5 - 3} = \frac{8}{2} = 4 </math>
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! Final Answer part a):
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!Final Answer part a): &nbsp;
 
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|Now that we have the slope of the line and a point on the line the equation for the line is <math> y - 6 = 4(x - 5)</math>. Another answer is <math> y + 2 = 4(x - 3)</math>. These answers are the same. They just look different.
 
|Now that we have the slope of the line and a point on the line the equation for the line is <math> y - 6 = 4(x - 5)</math>. Another answer is <math> y + 2 = 4(x - 3)</math>. These answers are the same. They just look different.
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! Final Answer part b):
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!Final Answer part b): &nbsp;
 
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|Since the slope of the line in part a) is 4, the slope of any line perpendicular to the answer in a) is <math> \frac{-1}{4}</math>
 
|Since the slope of the line in part a) is 4, the slope of any line perpendicular to the answer in a) is <math> \frac{-1}{4}</math>

Latest revision as of 00:01, 26 May 2015

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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