2.8 – Graphing Inequalities

2.8 – Graphing InequalitiesSteps for graphing inequalities:

2.8 – Graphing InequalitiesSteps for graphing inequalities:

1) Graph just like you would an equation:

2.8 – Graphing InequalitiesSteps for graphing inequalities:

1) Graph just like you would an equation:• Table

2.8 – Graphing InequalitiesSteps for graphing inequalities:

1) Graph just like you would an equation:• Table – used when eq. In slope-int. form

2.8 – Graphing InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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 InequalitiesSteps 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

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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 6If true, shade side of line with the origin.

Ex. 1 Graph 2x + 3y > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 6If true, shade side of line with the origin.If false, shade side of line w/o the origin.

Ex. 1 Graph 2x + 3y > 61) Graph just like the equation:

So, graph 2x + 3y = 6x-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 > 6If true, shade side of line with the origin.If false, shade side of line w/o the origin.

Ex. 2 Graph y ≤ x + 1

Ex. 2 Graph y ≤ x + 1

1) Graph y = x + 1

Ex. 2 Graph y ≤ x + 1

1) Graph y = x + 1

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (1,2)

Ex. 2 Graph y ≤ x + 1

1) Graph y = x + 1

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (1,2)

Ex. 2 Graph y ≤ x + 1

1) Graph y = x + 1

2) y ≤ x + 1, so use solid line!

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (1,2)

Ex. 2 Graph y ≤ x + 1

1) Graph y = x + 1

2) y ≤ x + 1, so use solid line!

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (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 ≤ 0 + 1

0 ≤ 1, TRUE!

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (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 ≤ 0 + 1

0 ≤ 1, TRUE!

x x + 1 y (x,y)

-1 -1 + 1 -2 (-1,0)

0 0 + 1 -1 (0,1)

1 1 + 1 0 (1,2)