2.8 – Graphing Inequalities. Steps for graphing inequalities:

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Presentation transcript:

2.8 – Graphing Inequalities

Steps for graphing inequalities:

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation:

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.  If false, shade side of line w/o the origin.

2.8 – Graphing Inequalities Steps for graphing inequalities: 1)Graph just like you would an equation: Table – used when eq. In slope-int. form x and y intercepts – used when in standard form 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.  Plug 0 in for x and plug 0 in for y!  If true, shade side of line with the origin.  If false, shade side of line w/o the origin.

Ex. 1 Graph 2x + 3y > 6

1)Graph just like the equation:

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int:

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0)

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int:

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2)

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y!

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

Ex. 1 Graph 2x + 3y > 6 1)Graph just like the equation: So, graph 2x + 3y = 6 x-int: 2x + 3(0) = 6 2x = 6 x = 3 (3,0) y-int: 2(0) + 3y = 6 3y = 6 y = 2 (0,2) 2)If ≥ or ≤, make the line solid. 3)If > or <, make the line dashed. 4)Plug the origin (0,0) into the inequality. Plug 0 in for x and plug 0 in for y! 2(0) + 3(0) > 6 0 > 6 If true, shade side of line with the origin. If false, shade side of line w/o the origin.

Ex. 2 Graph y ≤ x + 1

1)Graph y = x + 1

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 xx + 1y(x,y) (-1,0) (0,1) (1,2)

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 xx + 1y(x,y) (-1,0) (0,1) (1,2)

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! xx + 1y(x,y) (-1,0) (0,1) (1,2)

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! xx + 1y(x,y) (-1,0) (0,1) (1,2)

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! 3)Plug in the origin: 0 ≤ ≤ 1, TRUE! xx + 1y(x,y) (-1,0) (0,1) (1,2)

Ex. 2 Graph y ≤ x + 1 1)Graph y = x + 1 2)y ≤ x + 1, so use solid line! 3)Plug in the origin: 0 ≤ ≤ 1, TRUE! xx + 1y(x,y) (-1,0) (0,1) (1,2)