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# Graphing Linear Equations and Inequalities: Exercise Supplement

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

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## Exercise Supplement

### Section 6.1

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

### Section 6.2

#### 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.

### Section 6.3

#### 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

### Sections 6.3-6.5

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

### Section 6.4

#### 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.

### Section 6.6

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

### Section 6.7

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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