Lesson 9
Slopes and Equations for All Kinds of Lines
Let’s figure out the slope 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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155235Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=24198a2f4ca0281eb3b1705dadef5379352fc18aa39086fbe3333104c8db41b0)
Problem 2
Match each pair of points to the slope of the line that joins them.
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155235Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=cc5ea1fdb9326f98041f39e1725601026f079e6e121b48644947eeb8dd73a7aa)
- Point A, slope = \(\text-3\)
- Point A, slope = \(\frac {\text{-}1}{4}\)
- Point C, slope = \(\frac {\text{-}1}{2}\)
- Point E, slope = \(\frac {\text{-}2}{3}\)
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?
Problem 5
Write an equation for each line.
![4 lines on coordinate grid colored red, blue, green, yellow.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155235Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=f2beed86ccb20189ed5909604bf8af5c116d4cab950d2a7c1d7a6f6b596eb0f9)
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?