# 11.E: Graphs (Exercises)

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

\( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

### 11.1 - Use the Rectangular Coordinate System

#### Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.

- (1, 3), (3, 1)
- (2, 5), (5, 2)

In the following exercises, plot each point in a rectangular coordinate system and identify the quadrant in which the point is located.

- (a) (−1, −5) (b) (−3, 4) (c) (2, −3) (d) \(\left(1, \dfrac{5}{2}\right)\)
- (a) (3, −2) (b) (−4, −1) (c) (−5, 4) (d) \(\left(2, \dfrac{10}{3}\right)\)

#### Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

#### Verify Solutions to an Equation in Two Variables

In the following exercises, find the ordered pairs that are solutions to the given equation.

- 5x + y = 10
- (5, 1)
- (2, 0)
- (4, −10)

- y = 6x − 2
- (1, 4)
- \(\left(\dfrac{1}{3} , 0\right)\)
- (6, −2)

#### Complete a Table of Solutions to a Linear Equation in Two Variables

In the following exercises, complete the table to find solutions to each linear equation.

- y = 4x − 1

x | y | (x, y) |
---|---|---|

0 | ||

1 | ||

-2 |

- y = \(− \frac{1}{2}\)x + 3

x | y | (x, y) |
---|---|---|

0 | ||

1 | ||

-2 |

- x + 2y = 5

x | y | (x, y) |
---|---|---|

0 | ||

1 | ||

-1 |

- 3x − 2y = 6

x | y | (x, y) |
---|---|---|

0 | ||

0 | ||

-2 |

#### Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

- x + y = 3
- x + y = −4
- y = 3x + 1
- y = − x − 1

### 11.2 - Graphing Linear Equations

#### Recognize the Relation Between the Solutions of an Equation and its Graph

In the following exercises, for each ordered pair, decide (a) if the ordered pair is a solution to the equation. (b) if the point is on the line.

- y = − x + 4
- (0, 4)
- (−1, 3)
- (2, 2)
- (−2, 6)

- y = \(\frac{2}{3}\)x − 1
- (0, −1)
- (3, 1)
- (−3, −3)
- (6, 4)

#### Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

- y = 4x − 3
- y = −3x
- 2x + y = 7

#### Graph Vertical and Horizontal lines

In the following exercises, graph the vertical or horizontal lines.

- y = −2
- x = 3

### 11.3 - Graphing with Intercepts

#### Identify the Intercepts on a Graph

In the following exercises, find the x- and y-intercepts.

#### Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

- x + y = 5
- x − y = −1
- y = \(\frac{3}{4}\)x − 12
- y = 3x

#### Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

- −x + 3y = 3
- x + y = −2

#### Choose the Most Convenient Method to Graph a Line

In the following exercises, identify the most convenient method to graph each line.

- x = 5
- y = −3
- 2x + y = 5
- x − y = 2
- y = \(\frac{1}{2}\)x + 2
- y = \(\frac{3}{4}\)x − 1

### 11.4 - Understand Slope of a Line

#### Use Geoboards to Model Slope

In the following exercises, find the slope modeled on each geoboard.

In the following exercises, model each slope. Draw a picture to show your results.

- \(\frac{1}{3}\)
- \(\frac{3}{2}\)
- \(− \frac{2}{3}\)
- \(− \frac{1}{2}\)

#### Find the Slope of a Line from its Graph

In the following exercises, find the slope of each line shown.

#### Find the Slope of Horizontal and Vertical Lines

In the following exercises, find the slope of each line.

- y = 2
- x = 5
- x = −3
- y = −1

#### Use the Slope Formula to find the Slope of a Line between Two Points

In the following exercises, use the slope formula to find the slope of the line between each pair of points.

- (2, 1), (4, 5)
- (−1, −1), (0, −5)
- (3, 5), (4, −1)
- (−5, −2), (3, 2)

#### Graph a Line Given a Point and the Slope

In the following exercises, graph the line given a point and the slope.

- (2, −2); m = \(\frac{5}{2}\)
- (−3, 4); m = \(− \frac{1}{3}\)

#### Solve Slope Applications

In the following exercise, solve the slope application.

- A roof has rise 10 feet and run 15 feet. What is its slope?

### PRACTICE TEST

- Plot and label these points:
- (2, 5)
- (−1, −3)
- (−4, 0)
- (3, −5)
- (−2, 1)

- Name the ordered pair for each point shown.

- Find the x-intercept and y-intercept on the line shown.

- Find the x-intercept and y-intercept of the equation 3x − y = 6.
- Is (1, 3) a solution to the equation x + 4y = 12? How do you know?
- Complete the table to find four solutions to the equation y = − x + 1.

x | y | (x, y) |
---|---|---|

0 | ||

1 | ||

3 | ||

-2 |

- Complete the table to find three solutions to the equation 4x + y = 8.

x | y | (x, y) |
---|---|---|

0 | ||

0 | ||

3 |

In the following exercises, find three solutions to each equation and then graph each line.

- y = −3x
- 2x + 3y = −6

In the following exercises, find the slope of each line.

- Use the slope formula to find the slope of the line between (0, −4) and (5, 2).
- Find the slope of the line y = 2.
- Graph the line passing through (1, 1) with slope m = \(\frac{3}{2}\).
- A bicycle route climbs 20 feet for 1,000 feet of horizontal distance. What is the slope of the route?

### Contributors

Lynn Marecek (Santa Ana College) and MaryAnne Anthony-Smith (Formerly of Santa Ana College). This content is licensed under Creative Commons Attribution License v4.0 "Download for free at http://cnx.org/contents/fd53eae1-fa2...49835c3c@5.191."