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# Graphing Linear Equations and Inequalities: Exercise Supplement

Module by: Wade Ellis, Denny Burzynski. E-mail the authors

Summary: This module is from Elementary Algebra by Denny Burzynski and Wade Ellis, Jr. In this chapter the student is shown how graphs provide information that is not always evident from the equation alone. The chapter begins by establishing the relationship between the variables in an equation, the number of coordinate axes necessary to construct its graph, and the spatial dimension of both the coordinate system and the graph. Interpretation of graphs is also emphasized throughout the chapter, beginning with the plotting of points. The slope formula is fully developed, progressing from verbal phrases to mathematical expressions. The expressions are then formed into an equation by explicitly stating that a ratio is a comparison of two quantities of the same type (e.g., distance, weight, or money). This approach benefits students who take future courses that use graphs to display information. The student is shown how to graph lines using the intercept method, the table method, and the slope-intercept method, as well as how to distinguish, by inspection, oblique and horizontal/vertical lines. This module contains the exercise supplement for the chapter "Graphing Linear Equations and Inequalities in One and Two Variables".

## Exercise Supplement

### Graphing Linear Equations and Inequalities in One Variable ((Reference))

For the following problems, graph the equations and inequalities.

6x18=6 6x18=6

x=4 x=4

4x3=7 4x3=7

5x1=2 5x1=2

x= 3 5 x= 3 5

10x16<4 10x16<4

2y+15 2y+15

y2 y2

7a 12 2 7a 12 2

3x+412 3x+412

x 8 3 x 8 3

165x111 165x111

0<3y+99 0<3y+99

0y<3 0y<3

#### Exercise 10

5c 2 +1=7 5c 2 +1=7

### Plotting Points in the Plane ((Reference))

#### Exercise 11

Draw a coordinate system and plot the following ordered pairs.

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

#### Exercise 12

As accurately as possible, state the coordinates of the points that have been plotted on the graph.

### Graphing Linear Equations in Two Variables ((Reference))

#### Exercise 13

What is the geometric structure of the graph of all the solutions to the linear equation y=4x9 y=4x9 ?

a straight line

### Graphing Linear Equations in Two Variables ((Reference)) - Graphing Equations in Slope-Intercept Form ((Reference))

For the following problems, graph the equations.

yx=2 yx=2

y+x3=0 y+x3=0

2x+3y=6 2x+3y=6

2y+x8=0 2y+x8=0

#### Exercise 18

4(xy)=12 4(xy)=12

#### Exercise 19

3y4x+12=0 3y4x+12=0

y=3 y=3

y2=0 y2=0

x=4 x=4

x+1=0 x+1=0

x=0 x=0

y=0 y=0

### The Slope-Intercept Form of a Line ((Reference))

#### Exercise 26

Write the slope-intercept form of a straight line.

#### Exercise 27

The slope of a straight line is a


of the steepness of the line.

measure

#### Exercise 28

Write the formula for the slope of a line that passes through the points ( x 1 ,y ) 1 ( x 1 ,y ) 1 and ( x 2 ,y ) 2 ( x 2 ,y ) 2 .

For the following problems, determine the slope and y-intercept y-intercept of the lines.

#### Exercise 29

y=4x+10 y=4x+10

##### Solution

slope:4 y-intercept:( 0,10 ) slope:4 y-intercept:( 0,10 )

y=3x11 y=3x11

#### Exercise 31

y=9x1 y=9x1

##### Solution

slope:9 y-intercept:( 0,1 ) slope:9 y-intercept:( 0,1 )

y=x+2 y=x+2

#### Exercise 33

y=5x4 y=5x4

##### Solution

slope:5 y-intercept:( 0,4 ) slope:5 y-intercept:( 0,4 )

y=x y=x

#### Exercise 35

y=6x y=6x

##### Solution

slope:6 y-intercept:( 0,0 ) slope:6 y-intercept:( 0,0 )

3y=4x+9 3y=4x+9

#### Exercise 37

4y=5x+1 4y=5x+1

##### Solution

slope: 5 4 y-intercept:( 0, 1 4 ) slope: 5 4 y-intercept:( 0, 1 4 )

2y=9x 2y=9x

#### Exercise 39

5y+4x=6 5y+4x=6

##### Solution

slope: 4 5 y-intercept:( 0, 6 5 ) slope: 4 5 y-intercept:( 0, 6 5 )

#### Exercise 40

7y+3x=10 7y+3x=10

#### Exercise 41

6y12x=24 6y12x=24

##### Solution

slope:2 y-intercept:( 0,4 ) slope:2 y-intercept:( 0,4 )

#### Exercise 42

5y10x15=0 5y10x15=0

#### Exercise 43

3y+3x=1 3y+3x=1

##### Solution

slope:1 y-intercept:( 0, 1 3 ) slope:1 y-intercept:( 0, 1 3 )

7y+2x=0 7y+2x=0

#### Exercise 45

y=4 y=4

##### Solution

slope:0 y-intercept:( 0,4 ) slope:0 y-intercept:( 0,4 )

For the following problems, find the slope, if it exists, of the line through the given pairs of points.

#### Exercise 46

(5,2), (6,3) (5,2), (6,3)

#### Exercise 47

(8,2), (10,6) (8,2), (10,6)

slope:2 slope:2

#### Exercise 48

(0,5), (3,4) (0,5), (3,4)

#### Exercise 49

(1,4), (3,3) (1,4), (3,3)

##### Solution

slope: 7 2 slope: 7 2

#### Exercise 50

(0,0), (8,5) (0,0), (8,5)

#### Exercise 51

(6,1), (2,7) (6,1), (2,7)

##### Solution

slope: 3 2 slope: 3 2

#### Exercise 52

(3,2), (4,5) (3,2), (4,5)

#### Exercise 53

(4,7), (4,2) (4,7), (4,2)

No Slope

#### Exercise 54

(3,1), (4,1) (3,1), (4,1)

#### Exercise 55

( 1 3 , 3 4 ),( 2 9 , 5 6 ) ( 1 3 , 3 4 ),( 2 9 , 5 6 )

##### Solution

slope: 57 4 slope: 57 4

#### Exercise 56

Moving left to right, lines with


slope rise while lines with

slope decline.

#### Exercise 57

Compare the slopes of parallel lines.

##### Solution

The slopes of parallel lines are equal.

### Finding the Equation of a Line ((Reference))

For the following problems, write the equation of the line using the given information. Write the equation in slope-intercept form.

#### Exercise 58

Slope=4, y-intercept=5 Slope=4, y-intercept=5

#### Exercise 59

Slope=3, y-intercept=6 Slope=3, y-intercept=6

y=3x6 y=3x6

#### Exercise 60

Slope=1, y-intercept=8 Slope=1, y-intercept=8

#### Exercise 61

Slope=1, y-intercept=2 Slope=1, y-intercept=2

y=x2 y=x2

#### Exercise 62

Slope=5, y-intercept=1 Slope=5, y-intercept=1

#### Exercise 63

Slope=11, y-intercept=4 Slope=11, y-intercept=4

y=11x4 y=11x4

#### Exercise 64

Slope=2, y-intercept=0 Slope=2, y-intercept=0

#### Exercise 65

Slope=1, y-intercept=0 Slope=1, y-intercept=0

y=x y=x

#### Exercise 66

m=3, (4,1) m=3, (4,1)

#### Exercise 67

m=2, (1,5) m=2, (1,5)

y=2x+3 y=2x+3

#### Exercise 68

m=6, (5,2) m=6, (5,2)

#### Exercise 69

m=5, (2,3) m=5, (2,3)

y=5x+7 y=5x+7

#### Exercise 70

m=9, (4,7) m=9, (4,7)

#### Exercise 71

m=2, (0,2) m=2, (0,2)

y=2x+2 y=2x+2

#### Exercise 72

m=1, (2,0) m=1, (2,0)

#### Exercise 73

(2,3), (3,5) (2,3), (3,5)

y=2x1 y=2x1

#### Exercise 74

(4,4), (5,1) (4,4), (5,1)

#### Exercise 75

(6,1), (5,3) (6,1), (5,3)

y=2x+13 y=2x+13

#### Exercise 76

(8,6), (7,2) (8,6), (7,2)

#### Exercise 77

(3,1), (2,3) (3,1), (2,3)

##### Solution

y= 2 5 x+ 11 5 y= 2 5 x+ 11 5

#### Exercise 78

(1,4), (2,4) (1,4), (2,4)

#### Exercise 79

(0,5), (6,1) (0,5), (6,1)

##### Solution

y= 2 3 x5 y= 2 3 x5

#### Exercise 80

(2,1), (6,1) (2,1), (6,1)

#### Exercise 81

(5,7), (2,7) (5,7), (2,7)

##### Solution

y=7( zeroslope ) y=7( zeroslope )

#### Exercise 82

(4,1), (4,3) (4,1), (4,3)

#### Exercise 83

(1,1), (1,5) (1,1), (1,5)

##### Solution

x=1( noslope ) x=1( noslope )

#### Exercise 84

(0,4), (0,3) (0,4), (0,3)

#### Exercise 85

(0,2), (1,0) (0,2), (1,0)

##### Solution

y=2x+2 y=2x+2

For the following problems, reading only from the graph, determine the equation of the line.

#### Exercise 87

##### Solution

y= 2 3 x2 y= 2 3 x2

y=2 y=2

y=1 y=1

### Graphing Linear Inequalities in Two Variables ((Reference))

For the following problems, graph the inequalities.

yx+2 yx+2

#### Exercise 93

y< 1 2 x+3 y< 1 2 x+3

#### Exercise 94

y> 1 3 x3 y> 1 3 x3

2x+3y6 2x+3y6

2x+5y20 2x+5y20

#### Exercise 97

4xy+12>0 4xy+12>0

y2 y2

x<3 x<3

y0 y0

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