Graphing Inequalities

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Graphing Inequalities
Created by Kenny Kong HKIS 200
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Lesson Objectives

• Know that a row of numbers represented on a line
  is known as a number line.
• Know that an open circle on a number line
  indicates the endpoint is not included.
• Know that a closed circle on a number line
  indicates the endpoint is included and the number
  is the answer.
• Know that the arrow at the end of the line
  indicates that the line goes on forever and the
  answers are infinite.

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Lesson Objectives Cont

• Know that a linear inequality has two variables
  just like a linear equation.
• Know that a linear inequality has two parts a
  line and a shaded area.
• Know that graphing linear inequalities involve
  finding the boundary line and the shaded area on
  a coordinate plane.
• Know that graphing linear inequalities is similar
  to graphing linear equations by putting the
  equation in the form of y mx b.

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Lesson Objectives Cont

• Know that if the inequality symbol is lt or gt, the
  boundary line will be dotted.
• Know that if the inequality symbol is ? or ?, the
  boundary line will be solid.
• Know that if the inequality symbol is gt or ?, you
  will generally shade above the boundary line.
• Know that the inequality, y lt or gt a number, is
  the same as the inequality, y lt or gt 0x number,
  having slope of 0 and a y-intercept of the
  number.

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Lesson Objectives Cont

• Know that y lt or gt a number with slope is 0, the
  boundary line will always be a horizontal line.
• Know that the inequality, x lt or gt a number,
  cannot be written in y mx b form because it
  does not have a slope or a y-intercept.
• Know that x lt or gt a number with no slope or a
  y-intercept will always be a vertical line
  passing the number.

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What is a Number Line?

• A number line is a row of numbers represented on
  a line.

• The starting point is 0.

• If you move to the right of 0 on the number line,
  the numbers are positive and become increasingly
  larger.

• If you move to the left of 0, the numbers are
  negative and get increasingly smaller.

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Graphing Points and Lines on a Number Line

• Example to graph x 3
• Put a point on the number line at 3.

• Example to plot the point -5
• Put a point on the number line at -5.

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Graphing Points and Lines on a Number Line

• Example to graph the inequalities x gt 5,

• Put put an open circle on 5.

• Then draw a line and arrow to the right.

• The open circle shows that 5 is not an answer.

• The line shows that all the points greater than 5
  are answers.

• The arrow shows that the answers are endless
  (infinite).

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Graphing Points and Lines on a Number Line

• Example to graph the inequalities x ? -2,

• Put put an closed circle on -2.

• Then draw a line and arrow to the left.

• The closed circle shows that -2 is an answer.

• The line shows that all the points less than or
  equal to -2 are answers.

• The arrow shows that the answers are endless
  (infinite).

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Graphing Linear Inequalities

• A linear inequality has two variables just like a
  linear equation.
• A linear inequality has two parts a line and a
  shaded area.
• When you graph linear equations, your first step
  is to put the equation into y mx b
  form.
• Do the same with the linear inequality.

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Graphing Linear Inequalities

• If the inequality symbol is lt or gt, the boundary
  line will be .

dotted

• If the inequality symbol is ? or ?, the boundary
  line will be .

solid
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Example 2x y gt 1

• Subtract 2x from both sides of the inequality.

2x y gt 1
2x
2x

• Simplify both sides of the inequality.

y gt 1 2x

• Use the commutative property.

y gt -2x 1
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Graphing of y gt -2x 1

• Start with the y-intercept of 1.

• The slope is 2, which means 2/1, so from the
  y-intercept of 1, go down 2 and to the right 1.

• Connect the starting point like in either
  direction with a dash line to form the boundary
  line.

• Because the inequality is gt, you will shade above
  the line.

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Graphing of y ? -2x 1

• Start with the y-intercept of 1.

• The slope is 2, which means 2/1, so from the
  y-intercept of 1, go down 2 and to the right 1.

• Connect the starting point like in either
  direction with a solid line to form the boundary
  line.

• Because the inequality is ?, you will shade above
  the line.

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Graphing of y ? 1/2 x ? 1/2

• Start with the y-intercept of
  -1/2 .

• The slope is 1/2 , so from the y-intercept of
  -1/2 , go up 1 and to the right 2.

• Connect the starting point like in either
  direction with a dash line to form the boundary
  line.

• Because the inequality is ?, you will shade below
  the line.