# 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.

### 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?

- 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.

### 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?