# 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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|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>. | + | |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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|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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|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): | + | !Final Answer part a): |

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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): | + | !Final Answer part b): |

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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: |
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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: |
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Since the slope of a line passing through two points is , the slope of the line is |

Final Answer part a): |
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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 . Another answer is . These answers are the same. They just look different. |

Final Answer part b): |
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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 |