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)
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