*Essential Question: How can you graph a linear inequality in two variables?
1. SUBMIT your Homework
2. Open your online text (eBook) to pg. 269
Copy “Core Concept”
– Graphing a Linear Inequality in Two Variables (pg. 269)
- Read Through ALL Examples
Start Today’s Assignment – 5.6 (Day 1) pg. 271 #4 - 30 even
5.6 Graphing Linear Inequalities in Two Variables
Mr. Knighton January 23
When you’re finished:
-Ch. 5 IXL sections: O.1, O.2, O.5, O.8, O.10; P.1, P.2, P.3
-Skills Trainer: 5.1, 5.6
Lesson 5-6: Graphing Inequalities in 2 Variables
Mr. Knighton January 14
Tell whether the ordered pair is a solution of the inequality.
?
?
Write the inequality.
a.
Write the inequality.
b.
Simplify. 8 is equal to 8.
SOLUTION
It is often convenient to use the
origin as a test point. However,
you must choose a different test
point when the origin is on the
boundary line.
Write the inequality.
Step 3 Because (0, 0) is a solution, shade
the half-plane that contains (0, 0).
SOLUTION
Substitute.
Step 2 Test (0, 0).
(0, 0)
Write the inequality.
Step 3 Because (0, 0) is not a solution, shade the
half-plane that does not contain (0, 0).
Substitute.
?
Check
Simplify.
0 ≯ 2
SOLUTION
Step 2 Test (0, 0).
(0, 0)
You can spend at most $10 on grapes and apples for a fruit salad. Grapes cost $2.50 per pound, and apples cost $1 per pound. Write and graph an inequality that represents the amounts of grapes and apples you can buy. Identify and interpret two solutions of the inequality.
1. Understand the Problem You know the most that you can spend and the
prices per pound for grapes and apples. You are asked to write and graph
an inequality and then identify and interpret two solutions.
2. Make a Plan Use a verbal model to write an inequality that represents the
problem. Then graph the inequality. Use the graph to identify two
solutions. Then interpret the solutions.
3. Solve the Problem
Words
Variables Let x be pounds of grapes and y be pounds of apples.
Cost per
pound of
grapes
Pounds
of grapes
Cost per
pound of
apples
Pounds
of apples
Amount
you can
spend
SOLUTION
Step 2 Test (0, 0).
Write the inequality.
Substitute.
?
Step 3 Because (0, 0) is a solution, shade the half-plane that contains (0, 0).
One possible solution is (1, 6) because it lies in the shaded half-plane. Another possible solution is (2, 5) because it lies on the solid line. So, you can buy 1 pound of grapes and 6 pounds of apples, or 2 pounds of grapes and 5 pounds of apples.
Simplify.
(2, 5)
(1,6)
Check
?
✓
?
✓
4. Look Back Check your solutions by substituting them into the original
inequality, as shown.
One possible solution is (1, 6) because it lies in the shaded half-plane. Another possible solution is (2, 5) because it lies on the solid line. So, you can buy 1 pound of grapes and 6 pounds of apples, or 2 pounds of grapes and 5 pounds of apples.