section 6.5: linear inequalities. is the ordered pair a solution for y > x – 3? a) (1,2) how do...
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Section 6.5: Linear Inequalities
Is the ordered pair a solution for
y > x – 3?
A) (1,2) How do we know if (1,2) is a solution?
y > x - 3( ) > ( ) - 312
A) (1,2)
True: (1,2) is a solution.
2 > -2 True or False?
B) (-3,-7) y > x - 3( ) > ( ) - 3
B) (-3,-7)-7 -3 -7 > -6 True or False?
False: (-3,-7) is not a solution.
Jim has saved $48. He plans to use the money to buy some old books and movies at the Half-Price bookstore. Books cost $6 and movies cost $8.
Inequality:
Graphing Inequalities: Two-Variables
6b + 8m ≤ 48
Books and Movies
0
1
2
3
4
5
6
7
0 1 2 3 4 5 6 7 8 9
books
Mo
vie
sbooks movies
Steps to graph an inequality1. Graph like normal (slope and y-intercept)2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point (not on the line): Shade the truth
-5
0
5
-5 0 5
Slope = y-int =
Solid or dashed?
Test point =
¾ 2
SOLID
(0,0)y < ¾ x + 20 < ¾(0) + 20 < 2TRUE
y < ¾ x + 2
1. Graph like normal2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point (pt not on the line) Shade the truth
-5
0
5
-5 0 5
Steps to graph an inequality
Slope = y-int =
Solid or dashed?
Test point =
-2 3dashed
(0,0)
y < -2x + 30 < -2(0) + 30 < 3TRUE
y < - 2x + 3
Steps to graph an inequality1. Graph like normal (slope and y-intercept)2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
-5
0
5
-5 0 5
Slope = y-int =
Solid or dashed?
Test point =
3 0
SOLID
(4,4)y > 3x4 > 3(4)4 > 12FALSE
y > 3x
-5
0
5
-5 0 5
Steps to graph an inequality1. Graph like normal2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
Slope = y-int =
Solid or dashed?
Test point =
0 2
SOLID
(0,0)y > 2
0 >2
FALSE
y > 2
Steps to graph an inequality1. Graph like normal (slope and y-intercept)2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
Slope = y-int =
Solid or dashed?
Test point =
undefined
dashed
(4,4)x > 24 > 2
true
x> 2
-5
0
5
-5 0 5
1. Graph like normal 2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
Steps to graph an inequality
x-int = y-int =
Solid or dashed?
Test point =
4 -3dashed
(0,0)
3x – 4y > 123(0) - 4(0) > 120 > 12FALSE
3x – 4y > 12
-5
0
5
-5 0 5
1. Graph like normal 2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
Steps to graph an inequality
x-int = y-int =
Solid or dashed?
Test point =
4 -2SOLID
(0,0)
2x – 4y > 82(0) - 4(0) > 80 > 8FALSE
2x – 4y > 8
Steps to graph an inequality1. Graph like normal (slope and y-intercept)2. Line: Solid (≥, ≤) or Dashed (>, <)?3. Test point: Shade the truth
Slope = y-int =
Solid or dashed?
Test point =
-⅓ 1
dashed
(0,0)y > -⅓ x + 10 > -⅓(0) + 10 > 1FALSE
y > -⅓ x + 1
-5
0
5
-5 0 5
Which inequality represents the graph at the right?
A. y < 2x + 1 C. y > 2x + 1B. y < x + 1 D. y < 2x + 1
A. y < 2x + 1
Assignment for 6.5Pg 397: 8-11, 14-21, 22-34 evens, 37
Elimination or substitution worksheet (34 points)
1. (4,1) 2. (-1, 3)
3. (8,3) 4. (7, 2)
5. (12, 9) 6. (1, -5)
7. (3, 4) 8. (2, 2)
9. (1, 8) 10. (-4, 3)
11.(6, 3) 12. (4, -5)
13.(-3, -4) 14. (6, -5)
1. (2,-3) 2. (-1,-1) 3. (1,2)