# 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: |
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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 |