# 11.9: Graphs (Exercises)

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## 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. (1, 3), (3, 1)
2. (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.

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

1. 2. 3. 4. ### Verify Solutions to an Equation in Two Variables

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

1. 5x + y = 10
1. (5, 1)
2. (2, 0)
3. (4, −10)
2. y = 6x − 2
1. (1, 4)
2. $$\left(\dfrac{1}{3} , 0\right)$$
3. (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.

1. y = 4x − 1
x y (x, y)
0
1
-2
1. y = $$− \dfrac{1}{2}$$x + 3
x y (x, y)
0
1
-2
1. x + 2y = 5
x y (x, y)
0
1
-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.

1. x + y = 3
2. x + y = −4
3. y = 3x + 1
4. 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.

1. y = − x + 4
1. (0, 4)
2. (−1, 3)
3. (2, 2)
4. (−2, 6) 1. y = $$\dfrac{2}{3}$$x − 1
1. (0, −1)
2. (3, 1)
3. (−3, −3)
4. (6, 4) ### Graph a Linear Equation by Plotting Points

In the following exercises, graph by plotting points.

1. y = 4x − 3
2. y = −3x
3. 2x + y = 7

### Graph Vertical and Horizontal lines

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

1. y = −2
2. x = 3

## 11.3 - Graphing with Intercepts

### Identify the Intercepts on a Graph

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

1. 2. ### Find the Intercepts from an Equation of a Line

In the following exercises, find the intercepts.

1. x + y = 5
2. x − y = −1
3. y = $$\dfrac{3}{4}$$x − 12
4. y = 3x

### Graph a Line Using the Intercepts

In the following exercises, graph using the intercepts.

1. −x + 3y = 3
2. 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.

1. x = 5
2. y = −3
3. 2x + y = 5
4. x − y = 2
5. y = $$\dfrac{1}{2}$$x + 2
6. y = $$\dfrac{3}{4}$$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.

1. 2. 3. 4. In the following exercises, model each slope. Draw a picture to show your results.

1. $$\dfrac{1}{3}$$
2. $$\dfrac{3}{2}$$
3. $$− \dfrac{2}{3}$$
4. $$− \dfrac{1}{2}$$

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

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

1. 2. 3. 4. ### Find the Slope of Horizontal and Vertical Lines

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

1. y = 2
2. x = 5
3. x = −3
4. 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.

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

1. (2, −2); m = $$\dfrac{5}{2}$$
2. (−3, 4); m = $$− \dfrac{1}{3}$$

### Solve Slope Applications

In the following exercise, solve the slope application.

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

## PRACTICE TEST

1. Plot and label these points:
1. (2, 5)
2. (−1, −3)
3. (−4, 0)
4. (3, −5)
5. (−2, 1)
2. Name the ordered pair for each point shown. 1. Find the x-intercept and y-intercept on the line shown. 1. Find the x-intercept and y-intercept of the equation 3x − y = 6.
2. Is (1, 3) a solution to the equation x + 4y = 12? How do you know?
3. Complete the table to find four solutions to the equation y = − x + 1.
x y (x, y)
0
1
3
-2
1. 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.

1. y = −3x
2. 2x + 3y = −6

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

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

## Contributors and Attributions

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