Lesson 11
Equations of All Kinds of Lines
Problem 1
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 2
Draw the following lines and then write an equation for each.
- Slope is 0, \(y\)-intercept is 5
- Slope is 2, \(y\)-intercept is -1
- Slope is -2, \(y\)-intercept is 1
- Slope is \(\text-\frac{1}{2}\), \(y\)-intercept is -1
![Blank coordinate plane, x, negative 5 to 5 by 5, y negative 5 to 5 by 5.](https://cms-im.s3.amazonaws.com/iPTRQ7c4b6rdNi3V52YnGEeM?response-content-disposition=inline%3B%20filename%3D%228-8.3.C10.PP.allquadgraph1.png%22%3B%20filename%2A%3DUTF-8%27%278-8.3.C10.PP.allquadgraph1.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=20240727T002418Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b7f00483c978d53213d6aaaf003229e1700d9d186762c269a09eec9fe501812b)
Solution
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Problem 3
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=20240727T002418Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1e79f62389073d212d0c72726279e50f016c3635528cdf304e1eedac008c85a0)
Solution
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Problem 4
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 3, Lesson 7.)