Lesson 9
Slopes and Equations for All Kinds of Lines
Problem 1
For each graph, calculate the slope of the line.
![3 graphs of lines labeled A, B, C.](https://cms-im.s3.amazonaws.com/BJ9792zAz8qER8SBDjirYJLo?response-content-disposition=inline%3B%20filename%3D%228-8.3.C10.PP.3graphs.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C10.PP.3graphs.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000217Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c957fcdcd5725817f4875796c319e8e7d74629d680a729024fee5c92f6c14b97)
Solution
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Problem 2
Match each pair of points to the slope of the line that joins them.
Solution
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Problem 3
Draw a line with the given slope through the given point. What other point lies on that line?
![Coordinate grid with points A, B, C, D, E, F plotted.](https://cms-im.s3.amazonaws.com/QUnGju6aRPpieypRWZmTccgt?response-content-disposition=inline%3B%20filename%3D%228-8.3.C10.PP.graph1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C10.PP.graph1.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000217Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d1dd86804a247c4e9d6dfdbe40457101b42cc0bf50dbc8ec646d18490b99d305)
- Point A, slope = \(\text-3\)
- Point A, slope = \(\frac {\text{-}1}{4}\)
- Point C, slope = \(\frac {\text{-}1}{2}\)
- Point E, slope = \(\frac {\text{-}2}{3}\)
Solution
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Problem 4
Suppose you wanted to graph the equation \(y=\text-4x-1\).
- Describe the steps you would take to draw the graph.
- How would you check that the graph you drew is correct?
Solution
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Problem 5
Write an equation for each line.
![4 lines on coordinate grid colored red, blue, green, yellow.](https://cms-im.s3.amazonaws.com/3g3mX7W6faH3Qg2Gy8DMi4R8?response-content-disposition=inline%3B%20filename%3D%228-8.3.C11.PP.4lines.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C11.PP.4lines.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000217Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=460b776181bc92c2ff39fd8d9d32a2a0c7aae84577cbefa38847245c45331699)
Solution
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Problem 6
A publisher wants to figure out how thick their new book will be. The book has a front cover and a back cover, each of which have a thickness of \(\frac{1}{4}\) of an inch. They have a choice of which type of paper to print the book on.
- Bond paper has a thickness of \(\frac{1}{4}\) inch per one hundred pages. Write an equation for the width of the book, \(y\), if it has \(x\) hundred pages, printed on bond paper.
- Ledger paper has a thickness of \(\frac{2}{5}\) inch per one hundred pages. Write an equation for the width of the book, \(y\), if it has \(x\) hundred pages, printed on ledger paper.
- If they instead chose front and back covers of thickness \(\frac{1}{3}\) of an inch, how would this change the equations in the previous two parts?
Solution
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(From Unit 5, Lesson 6.)