9.5 inequalities and two variables goal(s): 1.to determine whether a given ordered pair is a...
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9.5 Inequalities and two variables
• Goal(s):
1. To determine whether a given ordered pair is a solution of an inequality
2. To graph inequalities in 2 variables
Is (2,3) a solution of 5x + 2y < 23 ?5(2) + 2(3) < 23
YES!
Is (2,1) a solution of x + y < 4 ?
(2) + (1) < 4
YES!
Is (4,8) a solution of y > 2x + 1 ?
(8) > 2(4) + 1
no
Is (-3,5) a solution of y > 2x + 1 ?
(5) > 2(-3) + 1
yes
Is (-3,458) a solution of y > 2x + 1 ?
Is (-3,19) a solution of y > 2x + 1 ?
Is (-3,6) a solution of y > 2x + 1 ?
Graph: 2x + 3y = 12
4
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
x y0
04
6
To Graph an Inequality• Use either the table method, x and y intercepts method, or
slope intercept method to graph (graph as if it was an =)• If it is a < or> the line will be a broken line and if it is a ≤
or ≥ the line will be solid• Pick an ordered pair that is not on the line• Plug the order pair into the inequality
- if it makes the inequality true shade in everything on that same side of the line
-if it makes the inequality false shade in everything on the opposite side of the line of the point
Graph: 2x + 3y 12
4
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
Is (1,1) a solution?Is (-4,2) a solution?Is (5,2) a solution?
x
Is (5,-2) a solution?Is (1,4) a solution?x
Is (0,0) a solution?Is (3,3) a solution? xIs (3,2) a solution?
half-planes
boundary line
To graph: 2x – 5y < 10• Graph the boundary line 2x – 5y = 10. Use a
dotted line for “< “ and a solid line for “”.• Determine which half-plane is the solution by
testing one point not on the boundary line. (0,0)
4
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
Graph: y – 2x 0• Graph the boundary line y – 2x = 10. Use a dotted
line for “< “ and a solid line for “”.• Determine which half-plane is the solution by
testing one point not on the boundary line. (0,0)
4
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
y = 2x + 0
Graph: x < 34
3
2
1
-1
-2
-3
-4
-6 -4 -2 2 4 6
To Identify the Inequality
• Identify the y-intercept (that is your b)
• Count out the slope (rise over run from left to right)
• Look for solid or dashed line
• Plug in an ordered pair from the shaded area into your choices and see which inequality is true
This graph represents which inequality?
1) 3 2
2) 3 2
3) 3 2
4) 3 2
y x
y x
y x
y x
1.Check (0,0)
2.Check “b”
3.Check slope + or neg
This graph represents which inequality?
1) 3 4 12
2) 3 4 12
3) 3 4 12
4) 3 4 12
x y
x y
x y
x y
1.Check (0,0)
2.Check x and y intercepts
3.Check dotted line
AssignmentPage 419
(2-40) eventake graph paper
Graph on white boards
1. X>3y
2. Y< x-5
3. X+ Y ≥3
4. 5X + 4Y ≤204 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46
4 3 2 1 -1 -2 -3 -4
-6-4
-22
46