lesson 6 mi/vocab half-plane boundary graph inequalities on the coordinate plane. solve real-world...
TRANSCRIPT
• half-plane
• boundary
• Graph inequalities on the coordinate plane.
• Solve real-world problems involving linear inequalities.
Graph an Inequality
Graph 2y – 4x > 6.
Step 1 Solve for y in terms of x.
Original inequality
Add 4x to each side.
Simplify.
Simplify.
Divide each side by 2.
Graph an Inequality
Step 2 Graph y = 2x + 3.
Since y > 2x +3 does not include values when y = 2x + 3, the boundary is not included in the solution set. The boundary should be drawn as a dashed line.
y > 2x +3 Original inequality0 > 2(0) +3 x = 0, y = 00 > 3 false
Step 3 Select a point in one of the half-planes and test it.Let’s use (0, 0).
Graph an Inequality
Answer: Since the statement is false, the half-plane containing the origin is not part of the solution. Shade the other half-plane.
Check Test a point in the other half-plane, for example, (–3, 1).
y > 2x + 3 Original inequality1 > 2(–3) + 3 x = –3, y = 11 > –3 Since the statement is true, the half-plane containing (–3, 1) should be shaded. The graph of the solution is correct.
JOURNALISM Lee Cooper writes and edits short articles for a local newspaper. It takes her about an hour to write an article and about a half-hour to edit an article. If Lee works up to 8 hours a day, how many articles can she write and edit in one day?
Write and Solve an Inequality
Explore You know how long it takes her to write and edit an article and how long she works each day.
Plan Let x equal the number of articles Lee can write. Let y equal the number of articles that Lee can edit. Write an open sentence representing the situation.
Write and Solve an Inequality
Number of articles she can write plus hour times
Number of articles she can edit
is up to 8 hours.
x + ● y ≤ 8
Solve Solve for y in terms of x.
Write and Solve an Inequality
Original inequality
Subtract x from each side.
Simplify.
Multiply each side by 2.
Simplify.
Since the open sentence includes the equation, graph y = –2x +16 as a solid line. Test a point in one of the half-planes, for example, (0, 0). Shade the half-plane containing (0, 0) since 0 ≤ –2(0) + 16 is true.
Write and Solve an Inequality
Answer:
Check Examine the situation.
Write and Solve an Inequality
Lee cannot work a negative number of hours. Therefore, the domain and range contain only nonnegative numbers.
Lee only wants to count articles that are completely written or completely edited. Thus, only points in the half-plane whose x- and y-coordinates are whole numbers are possible solutions.
One solution is (2, 3). This represents 2 written articles and 3 edited articles.
1. A
2. B
3. C
4. D
0%0%0%0%
A B C D
A. 2 chicken sandwiches,
2 tuna sandwiches
B. 1 chicken sandwich, 1 tuna sandwich
C. 4 chicken sandwich, 4 tuna sandwiches
D. 4 chicken sandwich, 10 tuna sandwiches
FOOD You offer to go to the local deli and pick up sandwiches for lunch. You have $30 to spend. Chicken sandwiches cost $3.00 each and tuna sandwiches are $1.50 each. How many sandwiches can you purchase for $30?