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AA Section 5-7
 

AA Section 5-7

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Graphing Inequalities in the Coordinate Plane

Graphing Inequalities in the Coordinate Plane

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    AA Section 5-7 AA Section 5-7 Presentation Transcript

    • Section 5-7 Graphing Inequalities in the Coordinate Plane
    • Warm-up Graph the following. 1. x ≤ 3 2. t > -4 3. y = 2x - 1
    • Warm-up Graph the following. 1. x ≤ 3 2. t > -4 x -2 -1 0 1 2 3 4 3. y = 2x - 1
    • Warm-up Graph the following. 1. x ≤ 3 2. t > -4 x t -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 3. y = 2x - 1
    • Warm-up Graph the following. 1. x ≤ 3 2. t > -4 x t -2 -1 0 1 2 3 4 -5 -4 -3 -2 -1 0 1 3. y = 2x - 1 y x
    • Half-plane:
    • Half-plane: A region formed on a plane when a line is placed on it
    • Half-plane: A region formed on a plane when a line is placed on it Boundary:
    • Half-plane: A region formed on a plane when a line is placed on it Boundary: The line that divides the plane in half
    • Example 1 Graph y < 3 on a coordinate plane.
    • Example 1 Graph y < 3 on a coordinate plane.
    • Example 1 Graph y < 3 on a coordinate plane. (This is the INEQUALZ app on the TI-84)
    • Graphing Linear Inequalities
    • Graphing Linear Inequalities 1. Treat inequalities as if the were equations, yet be mindful of the signs
    • Graphing Linear Inequalities 1. Treat inequalities as if the were equations, yet be mindful of the signs 2. Graph the boundary line *Dashed for <, >, ≠ *Solid for ≤, ≥
    • Graphing Linear Inequalities 1. Treat inequalities as if the were equations, yet be mindful of the signs 2. Graph the boundary line *Dashed for <, >, ≠ *Solid for ≤, ≥ 3. Shade appropriately *Check points *When in “slope-intercept” form, the sign will tell you to shade above or below the boundary line
    • Example 2 Graph y ≥ 4/3 x + 5
    • Example 2 Graph y ≥ 4/3 x + 5
    • Lattice Points
    • Lattice Points Points whose coordinates are integers
    • Example 3 Matt Mitarnowski has at most $1.50 in his pocket. a. Draw a graph showing all possible combinations of dimes and quarters Matt could have.
    • Example 3 Matt Mitarnowski has at most $1.50 in his pocket. a. Draw a graph showing all possible combinations of dimes and quarters Matt could have. 15.0 12.5 10.0 Dimes 7.5 5.0 2.5 0 0 1 2 3 4 5 6 Quarters
    • Example 3 b. How many coordinates are there?
    • Example 3 b. How many coordinates are there? 58 total possible combinations of quarters and dimes
    • Homework
    • Homework p. 316 #1 - 26 “To have a right to do a thing is not at all the same as to be right in doing it.” - GK Chesterton