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Mathematics LibreTexts

7.10: Exercise Supplement

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Exercise Supplement

Graphing Linear Equations and Inequalities in One Variable

For the following problems, graph the equations and inequalities.

Exercise 7.10.1

6x18=6

A horizontal line with arrows on both ends labeled as x.

Answer

x=4

A number line with arrows on each end, labeled from negative two to four in increments of one. There is a closed circle at four.

Exercise 7.10.2

4x3=7

A horizontal line with arrows on both ends labeled as x.

Exercise 7.10.3

5x1=2

A horizontal line with arrows on both ends labeled as x.

Answer

x=35

A number line with arrows on each end, labeled from negative one to ttwo in increments of one. There is a closed circle at three over five.

Exercise 7.10.4

10x16<4

A horizontal line with arrows on both ends labeled as x.

Exercise 7.10.5

2y+15

A horizontal line with arrows on both ends labeled as y.

Answer

y2

Exercise 7.10.6

7a122

A horizontal line with arrows on both ends labeled as a.

Exercise 7.10.7

3x+412

A horizontal line with arrows on both ends labeled as x.

Answer

x83

A number line with arrows on each end, labeled from negative two to three, in increments of one. There is a closed circle at a point between two and three. A dark line is orginating from this circle and heading towards the left of it.

Exercise 7.10.8

165x111

A horizontal line with arrows on both ends labeled as x.

Exercise 7.10.9

0<3y+99

A horizontal line with arrows on both ends labeled as y.

Answer

0y<3

A number line with arrows on each end, labeled from negative one to four, in increments of one. There is a closed circle at zero and an open circle at three. These circles are connected by a a black line.

Exercise 7.10.10

5c2+1=7

A horizontal line with arrows on both ends labeled as c.

Plotting Points in the Plane

Exercise 7.10.11

Draw a coordinate system and plot the following ordered pairs.

(3,1),(4,2),(1,3),(0,3),(3,0),(5,23)

Answer

Total six points plotted in an xy-coordinate plane. The coordinates of these points are negative one, negative three; zero, three; three, one; three, zero; four, negative two; and five, negative two over three.

Exercise 7.10.12

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

Total seven points plotted on an xy-plane. The coordinates of these points are one, three; two, one; three,zero; three, negative two; negative one, negative three; negative three, three.

Graphing Linear Equations in Two Variables

Exercise 7.10.13

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

Answer

a straight line

Graphing Linear Equations in Two Variables - Graphing Equations in Slope-Intercept Form

For the following problems, graph the equations.

Exercise 7.10.14

yx=2

Exercise 7.10.15

y+x3=0

Answer

A graph of a line passing through two points with coordinates zero, three and five, zero.

Exercise 7.10.16

2x+3y=6

Exercise 7.10.17

2y+x8=0

Answer

A graph of a line passing through two points with coordinates zero, four and eight, zero.

Exercise 7.10.18

4(xy)=12

Exercise 7.10.19

3y4x+12=0

Answer

A graph of a line passing through two points with coordinates zero, three and negative four, zero.

Exercise 7.10.20

y=3

Exercise 7.10.21

y2=0

Answer

A graph of a line parallel to x-axis in an xy plane. The line is labeled as ' y equals two'. The line crosses the y-axis at y equals two.

Exercise 7.10.22

x=4

Exercise 7.10.23

x+1=0

Answer

A graph of a line parallel to y-axis in an xy plane. The line is labeled as 'x equals negative one'. The line crosses the x-axis at x equals negative one.

Exercise 7.10.24

x=0

Exercise 7.10.25

y=0

Answer

A graph of a line in an xy plane coincident to x-axis labeled as 'y equals zero'.

The Slope-Intercept Form of a Line

Exercise 7.10.26

Write the slope-intercept form of a straight line.

Exercise 7.10.27

The slope of a straight line is a ____ of the steepness of the line.

Answer

measure

Exercise 7.10.28

Write the formula for the slope of a line that passes through the points (x1,y1) and (x2,y2).

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

Exercise 7.10.29

y=4x+10

Answer

slope:  4

y-intercept:  (0,10)

Exercise 7.10.30

y=3x11

Exercise 7.10.31

y=9x1

Answer

slope:  9

y-intercept:  (0,1)

Exercise 7.10.32

y=x+2

Exercise 7.10.33

y=5x4

Answer

slope:  5

y-intercept:  (0,4)

Exercise 7.10.34

y=x

Exercise 7.10.35

y=6x

Answer

slope:  6

y-intercept:  (0,0)

Exercise 7.10.36

3y=4x+9

Exercise 7.10.37

4y=5x+1

Answer

slope:  54

y-intercept:  (0,14)

Exercise 7.10.38

2y=9x

Exercise 7.10.39

5y+4x=6

Answer

slope:  45

y-intercept:  (0,65)

Exercise 7.10.40

7y+3x=10

Exercise 7.10.41

6y12x=24

Answer

slope:  2

y-intercept:  (0,4)

Exercise 7.10.42

5y10x15=0

Exercise 7.10.43

3y+3x=1

Answer

slope:  1

y-intercept:  (0,13)

Exercise 7.10.44

7y+2x=0

Exercise 7.10.45

y=4

Answer

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 7.10.46

(5,2),(6,3)

Exercise 7.10.47

(8,2),(10,6)

Answer

slope: 2

Exercise 7.10.48

(0,5),(3,4)

Exercise 7.10.49

(1,4),(3,3)

Answer

slope: 72

Exercise 7.10.50

(0,0),(8,5)

Exercise 7.10.51

(6,1),(2,7)

Answer

slope:  32

Exercise 7.10.52

(3,2),(4,5)

Exercise 7.10.53

(4,7),(4,2)

Answer

No Slope

Exercise 7.10.54

(3,1),(4,1)

Exercise 7.10.55

(13,34),(29,56)

Answer

slope: 574

Exercise 7.10.56

Moving left to right, lines with slope rise while lines with slope decline.

Exercise 7.10.57

Compare the slopes of parallel lines.

Answer

The slopes of parallel lines are equal.

Finding the Equation of a Line

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

Exercise 7.10.58

Slope=4, y-intercept=5

Exercise 7.10.59

Slope=3, y-intercept=6

Answer

y=3x6

Exercise 7.10.60

Slope=1, y-intercept=8

Exercise 7.10.61

Slope=1, y-intercept=2

Answer

y=x2

Exercise 7.10.62

Slope=5, y-intercept=1

Exercise 7.10.63

Slope=11, y-intercept=4

Answer

y=11x4

Exercise 7.10.64

Slope=2, y-intercept=0

Exercise 7.10.65

Slope=1, y-intercept=0

Answer

y=x

Exercise 7.10.66

m=3,(4,1)

Exercise 7.10.67

m=2,(1,5)

Answer

y=2x+3

Exercise 7.10.68

m=6,(5,2)

Exercise 7.10.69

m=5,(2,3)

Answer

y=5x+7

Exercise 7.10.70

m=9,(4,7)

Exercise 7.10.71

m=2,(0,2)

Answer

y=2x+2

Exercise 7.10.72

m=1,(2,0)

Exercise 7.10.73

(2,3),(3,5)

Answer

y=2x1

Exercise 7.10.74

(4,4),(5,1)

Exercise 7.10.75

(6,1),(5,3)

Answer

y=2x+13

Exercise 7.10.76

(8,6),(7,2)

Exercise 7.10.77

(3,1),(2,3)

Answer

y=25x+115

Exercise 7.10.78

(1,4),(2,4)

Exercise 7.10.79

(0,5),(6,1)

Answer

y=23x5

Exercise 7.10.80

(2,1),(6,1)

Exercise 7.10.81

(5,7),(2,7)

Answer

y=7 (zero slope)

Exercise 7.10.82

(4,1),(4,3)

Exercise 7.10.83

(1,1),(1,5)

Answer

x=1 (no slope)

Exercise 7.10.84

(0,4),(0,3)

Exercise 7.10.85

(0,2),(1,0)

Answer

y=2x+2

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

Exercise 7.10.86

A graph of a line sloped up and to the right. The line crosses the y-axis at y equals one, and crosses the x-axis at x equals negative two.

Exercise 7.10.87

A graph of a line sloped up and to the right. The line crosses the x-axis at x equals three, and crosses the y-axis at y equals negative two.

Answer

y=23x2

Exercise 7.10.88

A graph of a line sloped down and to the right. The line crosses the y-axis at y equals one, and crosses the x-axis at x equals four.

Exercise 7.10.89

A graph of a parallel to x-axis. The line crosses the y-axis at y equals negative two.

Answer

y=2

Exercise 7.10.90

A graph of a parallel to y-axis. The line crosses the x-axis at x equals three.

Exercise 7.10.91

A graph of a parallel to x-axis. The line crosses the y-axis at y equals one.

Answer

y=1

Graphing Linear Inequalities in Two Variables

For the following problems, graph the inequalities.

Exercise 7.10.92

yx+2

An xy-plane with gridlines, labeled negative five and five on the both axes.

Exercise 7.10.93

y<12+3

An xy-plane with gridlines, labeled negative five and five on the both axes.

Answer

A line in an xy plane passing through two points with coordinates zero, three and four, one. The region below the line is shaded.

Exercise 7.10.94

y>13x3

An xy-plane with gridlines, labeled negative five and five on the both axes.

Exercise 7.10.95

2x+3y6

An xy-plane with gridlines, labeled negative five and five on the both axes.

Answer

A line in an xy plane passing through two points with coordinates zero, negative two and three, zero. The region below the line is shaded.

Exercise 7.10.96

2x+5y20

An xy-plane with gridlines, labeled negative five and five on the both axes.

Exercise 7.10.97

4xy+12>0

An xy-plane with gridlines, labeled negative five and five on the both axes.

Answer

A line in an xy plane passing through two points with coordinates zero, twelve and three, zero. The region to the right of the line is shaded.

Exercise 7.10.98

y2

An xy-plane with gridlines, labeled negative five and five on the both axes.

Exercise 7.10.99

x<3

An xy-plane with gridlines, labeled negative five and five on the both axes.

Answer

A dashed line parallel to y-axis in an xy plane. The line crosses the x-axis at x equals three. The region to the left of the line is shaded.

Exercise 7.10.100

y0

An xy-plane with gridlines, labeled negative five and five on the both axes.


This page titled 7.10: Exercise Supplement is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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