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Graphing Inequalities

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Know that a linear inequality has two variables just like a linear equation. ... The line shows that all the points less than or equal to -2 are answers. ... – PowerPoint PPT presentation

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Title: Graphing Inequalities


1
Graphing Inequalities
Created by Kenny Kong HKIS 200
3
2
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.

3
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.

4
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.

5
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.

6
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.

7
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.

8
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).

9
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).

10
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.

11
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
12
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
13
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.

14
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.

15
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.
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