Today: Warm-Up Graphing Inequalities Khan Academy Due Tomorrow Class Work TGIF January11, 2013
Today:
Warm-UpGraphing
InequalitiesKhan Academy Due Tomorrow
Class Work
TGIF January11, 2013
Warm-Up
1.
2. The perimeter of a triangle is 51". The longest side is twice the length of the shortest. The third side is 3 inches longer than the shortest side. Write an equation then find the length of each side.
3. 4. What percent of 60 is 45?
5.
Objective- To graph inequalities on the coordinate plane.
Recall…Graph n < 3 on a number line.
-3 -2 -1 0 1 2 3 4
Tell whether the ordered pair is a solution of the inequality.
Identifying Solutions of Inequalities
(–2, 4); y < 2x + 1
Substitute (–2, 4) for (x, y).y < 2x + 1
4 2(–2) + 1
4 –4 + 14 –3<
(–2, 4) is not a solution.
a. (4, 5); y < x + 1
Tell whether the ordered pair is a solution of the inequality.
y < x + 1 Substitute (4, 5) for (x, y).
Substitute (1, 1) for (x, y).
b. (1, 1); y > x – 7
y > x – 7
5 4 + 15 5 <
1 1 – 7>1 –6
(4, 5) is not a solution. (1, 1) is a solution.
Vocabulary:
Half-plane: The region of a graph on one side of a boundary.Boundary: A boundary of an inequality is a line that separates the coordinate plane into half-planes.
A solid line (shown), includes the points on the line. The inequality is < or >.
A dashed line does not include the points on the line. The inequality is < or >.
Graphing Linear Inequalities
Step 1
Solve the inequality for y (slope-intercept form).
Step 2
Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >.
Step 3
Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer.
Class Notes & Practice Problems:
Graphing Linear Inequalities
Graph y > 3 on the coordinate plane.
x
y
x
y
Graph x < -2 on the coordinate plane.
Graphing Linear Inequalities
Graph y > -3x + 2 on the coordinate plane.
x
yBoundary Line
y = -3x + 2
m = -3
b = 2
Test a point not on the linetest (0,0)
0 > -3(0) + 2
Not true!
Graphing Linear Inequalities
Graph the solutions of the linear inequality.5x + 2y >
–8 Step 1 Solve the inequality for y.Step 2 Graph the boundary
line and Use a dashed line for >. y = x – 4.
Step 3: Test a point not on the line. Use (0,0) when you can.5(0) + 2(0) > -8, True or False?If true, include that point in your shading.
Graph y -3x + 2 on the coordinate plane.
x
y
Instead of testing a point
If in y = mx + b form...
Shade up
Shadedown
Solid line
Dashed line
> <
Graphing Linear Inequalities
Graph on the coordinate plane.
3x - 4y > 12-3x -3x-4y > -3x + 12-4 -4
y < x - 33
4
m =
b = -3
3
4
Boundary Linex
y
Graphing Linear Inequalities
Notes & Review
Shade the Solution Set
If the point makes the inequality
true, shade that side of the line.
If the point does not make the
inequality true, shade the opposite
side of the line.
Notes & Review
Class Work:Pages 71-72; All
When dealing with angled lines,If the inequality is > or > ,then you shade
above
Graphing Linear Inequalities
If the inequality is < or < ,then you shade below
ProblemIf you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have.
Let n = # of nickelsLet d = # of dimes
0.05 n + 0.10 d < 5.00
or
5 n + 10 d < 500
Graphing Linear Inequalities
5n + 10d < 500n d
0 50
100 0
0 10 20 30 40 50 60 70 80 90 100n
d
60
50
40
30
20
10
0