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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 ( [link] )

For the following problems, graph the equations and inequalities.

2 y + 1 5
A horizontal line with arrows on both ends labeled as y.

y 2

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

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3 x + 4 12
A horizontal line with arrows on both ends labeled as x.

x 8 3

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.

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16 5 x 1 11
A horizontal line with arrows on both ends labeled as x.

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0 < 3 y + 9 9
A horizontal line with arrows on both ends labeled as y.

0 y < 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.

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Plotting points in the plane ( [link] )

Draw a coordinate system and plot the following ordered pairs.

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



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.

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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.

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Graphing linear equations in two variables ( [link] )

What is the geometric structure of the graph of all the solutions to the linear equation y = 4 x 9 ?

a straight line

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Graphing linear equations in two variables ( [link] ) - graphing equations in slope-intercept form ( [link] )

For the following problems, graph the equations.

The slope-intercept form of a line ( [link] )

Write the slope-intercept form of a straight line.

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

measure

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

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

y = 4 x + 10

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

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y = 9 x 1

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

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y = 5 x 4

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

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y = 6 x

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

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4 y = 5 x + 1

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

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5 y + 4 x = 6

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

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6 y 12 x = 24

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

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3 y + 3 x = 1

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

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y = 4

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

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

( 8 , 2 ) , ( 10 , 6 )

slope: 2

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( 1 , 4 ) , ( 3 , 3 )

slope: 7 2

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( 0 , 0 ) , ( 8 , 5 )

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( 6 , 1 ) , ( 2 , 7 )

slope: 3 2

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( 3 , 2 ) , ( 4 , 5 )

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( 4 , 7 ) , ( 4 , 2 )

No Slope

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( 3 , 1 ) , ( 4 , 1 )

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

slope: 57 4

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

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Compare the slopes of parallel lines.

The slopes of parallel lines are equal.

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Finding the equation of a line ( [link] )

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

Slope= 4 , y -intercept= 5

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Slope= 3 , y -intercept= 6

y = 3 x 6

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Slope= 1 , y -intercept= 8

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Slope= 1 , y -intercept= 2

y = x 2

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Slope= 5 , y -intercept= 1

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Slope= 11 , y -intercept= 4

y = 11 x 4

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Slope= 2 , y -intercept= 0

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Slope= 1 , y -intercept= 0

y = x

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m = 2 , ( 1 , 5 )

y = 2 x + 3

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m = 5 , ( 2 , 3 )

y = 5 x + 7

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m = 9 , ( 4 , 7 )

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m = 2 , ( 0 , 2 )

y = 2 x + 2

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( 2 , 3 ) , ( 3 , 5 )

y = 2 x 1

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( 6 , 1 ) , ( 5 , 3 )

y = 2 x + 13

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( 3 , 1 ) , ( 2 , 3 )

y = 2 5 x + 11 5

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( 1 , 4 ) , ( 2 , 4 )

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( 0 , 5 ) , ( 6 , 1 )

y = 2 3 x 5

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( 5 , 7 ) , ( 2 , 7 )

y = 7 ( zero slope )

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( 1 , 1 ) , ( 1 , 5 )

x = 1 ( no slope )

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( 0 , 4 ) , ( 0 , 3 )

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( 0 , 2 ) , ( 1 , 0 )

y = 2 x + 2

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

Graphing linear inequalities in two variables ( [link] )

For the following problems, graph the inequalities.

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Source:  OpenStax, Elementary algebra. OpenStax CNX. May 08, 2009 Download for free at http://cnx.org/content/col10614/1.3
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