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Graph the linear inequality y > 4 x .

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Graph the linear inequality y > x .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals x is plotted as a solid line extending from the bottom left toward the top right. The region above the line is shaded.

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Graph the linear inequality y x .

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Graph the linear inequality y −3 x .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x is plotted as a solid line extending from the top left toward the bottom right. The region to the left of the line is shaded.

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Graph the linear inequality y −2 .

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Graph the linear inequality y < −1 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 1 is plotted as a dashed horizontal line. The region below the line is shaded.

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Graph the linear inequality y < 4 .

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Graph the linear inequality y 2 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals 2 is plotted as a solid horizontal line. The region above the line is shaded.

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Graph the linear inequality x 5 .

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Graph the linear inequality x > −2 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 2 is plotted as a dashed vertical line. The region to the right of the line is shaded.

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Graph the linear inequality x > −3 .

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Graph the linear inequality x 4 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals 4 is plotted as a solid vertical line. The region to the left of the line is shaded.

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Graph the linear inequality x y < 4 .

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Graph the linear inequality x y < −3 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x minus y equals negative 3 is plotted as a dashed line extending from the bottom left toward the top right. The region above the line is shaded.

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Graph the linear inequality y 3 2 x .

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Graph the linear inequality y 5 4 x .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals five-fourths x is plotted as a solid line extending from the bottom left toward the top right. The region below the line is shaded.

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Graph the linear inequality y > −2 x + 1 .

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Graph the linear inequality y < −3 x 4 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line y equals negative 3 x minus 4 is plotted as a dashed line extending from the top left toward the bottom right. The region to the left of the line is shaded.

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Graph the linear inequality x −1 .

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Graph the linear inequality x 0 .

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 10 to 10. The line x equals negative 0 is plotted as a solid vertical line along the y-axis. The region to the right of the line is shaded.

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Everyday math

Money. Gerry wants to have a maximum of $100 cash at the ticket booth when his church carnival opens. He will have $1 bills and $5 bills. If x is the number of $1 bills and y is the number of $5 bills, the inequality x + 5 y 100 models the situation.

  1. Graph the inequality.
  2. List three solutions to the inequality x + 5 y 100 where both x and y are integers.
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Shopping. Tula has $20 to spend at the used book sale. Hardcover books cost $2 each and paperback books cost $0.50 each. If x is the number of hardcover books Tula can buy and y is the number of paperback books she can buy, the inequality 2 x + 1 2 y 20 models the situation.

  1. Graph the inequality.
  2. List three solutions to the inequality 2 x + 1 2 y 20 where both x and y are whole numbers.

  1. The graph shows the x y-coordinate plane. The x- axis runs from 0 to 20 and the y-axis runs from 0 to 30. The line 2 x plus one-half y equals 20 is plotted as a solid line extending from the top left toward the bottom right. The region below the line is shaded.

  2. Answers will vary.
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Writing exercises

Lester thinks that the solution of any inequality with a>sign is the region above the line and the solution of any inequality with a<sign is the region below the line. Is Lester correct? Explain why or why not.

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Explain why in some graphs of linear inequalities the boundary line is solid but in other graphs it is dashed.

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Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This is a table that has four rows and four columns. In the first row, which is a header row, the cells read from left to right: “I can…,” “confidently,” “with some help,” and “no-I don’t get it!” The first column below “I can…” reads “verify solutions to an inequality in two variables,”, “recognize the relation between the solutions of an inequality and its graph,” and “graph linear inequalities.” The rest of the cells are blank.

What does this checklist tell you about your mastery of this section? What steps will you take to improve?

Rectangular Coordinate System

Plot Points in a Rectangular Coordinate System

In the following exercises, plot each point in a rectangular coordinate system.


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

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( 4 , 3 )
( −4 , 3 )
( −4 , −3 )
( 4 , −3 )

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (4, 3) is plotted and labeled

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

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

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (2, three halves) is plotted and labeled

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Identify Points on a Graph

In the following exercises, name the ordered pair of each point shown in the rectangular coordinate system.

The graph shows the x y-coordinate plane. The x- and y-axes each run from negative 6 to 6. The point (2, 0) is plotted and labeled

( 2 , 0 ) ( 0 , −5 ) ( −4.0 ) ( 0 , 3 )

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Verify Solutions to an Equation in Two Variables

In the following exercises, which ordered pairs are solutions to the given equations?

5 x + y = 10

( 5 , 1 )
( 2 , 0 )
( 4 , −10 )

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y = 6 x 2

( 1 , 4 )
( 1 3 , 0 )
( 6 , −2 )

a, b

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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.

y = 4 x 1

x y ( x , y )
0
1
−2
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y = 1 2 x + 3

x y ( x , y )
0
4
−2
x y ( x , y )
0 3 ( 0 , 3 )
4 1 (4, 1)
−2 4 ( −2 , 4 )
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x + 2 y = 5

x y ( x , y )
0
1
−1
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3 x + 2 y = 6

x y ( x , y )
0
0
−2
x y ( x , y )
0 −3 ( 0 , −3 )
2 0 ( 2 , 0 )
−2 −6 ( −2 , −6 )
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Find Solutions to a Linear Equation in Two Variables

In the following exercises, find three solutions to each linear equation.

Practice Key Terms 3

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Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
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