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Day 2 and 3 Graphing Linear Inequalities in Two Variables.notebook
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Formative Quiz1) Sketch the graph of the following linear equation.
(a)
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(b)
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2. Solve for x in the given triangle.
12
530
x470
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3. Solve for x in the given triangle.
x870
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Graphing Linear Inequalities in Two Variables
Linear Inequality – a linear inequality is a relationship between two linear expressions in which one expression is less than, greater than, less than or equal to, or greater than or equal to the other expression.
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Inequalities:
> greater than < less than≤ less than or equal to≥ greater than or equal to
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List some ordered pairs (x and y values) that make this inequality true.
(2,0) is an ordered pair that makes this inequality true:
y < 2x 3
0 < 2(2) 3
0 < 4 3
0 < 1
This is true, so (2,0) would be in the shaded region of the graph of y < 2x 3.
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Solving Inequalities
• Rearranging inequalities is much like rearranging equations.
• However, there are times when you must reverse the inequality sign to keep the inequality true.
i.e.
If you divide or multiply both sides of the inequality by a negative number, the inequality sign must be
reversed.
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Solve the following inequalities for y:1) 2)
3) 4)
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Half plane: the region on one side of the graph of a linear relation on a Cartesian plane
Solution Region: The part of the graph of a linear inequality that represents the solution set (the set of all possible solutions).
"Greater Than" so shade above. "Less Than" so shade below.
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Neither includes = so give it a dotted line.
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Domain: All the possible values for "x"
Range: All the possible values for "y"
Every Equation & Graph has Domain & Range Values:
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Number SetsReal Numbers (R): Any kind of number found on a
number line including positives, negatives, decimals, fractions,...
Natural Numbers (N): Counting numbers starting at 1 (1, 2, 3,.....)
Whole Numbers (W): Counting numbers starting at 0(0, 1, 2, 3,....)
Integers (I): Counting numbers including negatives(...3, 2, 1, 0, 1, 2, 3,....)
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Since the domain and range are not given, it's assumed that they are real numbers.
It could also written in set notation
This produces a solution set that is continuous. Continuous means that answers include things that are measurable, such as time. It also means that your answers can be represented by decimals.
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How would your graph change if the set notation changed to the following?
not equal to
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Try these ones:
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horizontal line
y = 6 , y ∈ Rvertical line
x = 4 , x ∈ R
Sketch the graph of each below where x ∈ R and y ∈ R.
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Horizontal Line Inequality
Sketch the graph of y ≥ 3 if y ∈ R.
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Discrete – consisting of separate or distinct parts; discrete variables represent things that can be counted, such as people in a room.
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Vertical Line Inequality
HINT: The graph of this inequality will be discrete. To show this we will need to stipple the boundary and shaded region which shows it is discrete. This means that you do not shade the entire area, but only shade specific dots for the solution.
Since X and Y can only be Integers, we can only shade the nice corner points and nothing in between that would NOT be Integers.
Sketch the solution set of x ≤ -8 if x ∈ I .
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Example: Graph the solution set for the inequalities:
for: y ∈ Ra) 3y + 6 ≥ 6 + y
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b) for: x ∈ I and y ∈ I
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c) 3x ≥ 12 4y , for: x ∈ R and y ∈ R
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d) ; for: x ∈ I and y ∈ I
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Example: A sports store has a net revenue of $100 on every pair of downhill skis sold and $120 on every pair of snow boards sold. The manager's goal is to have revenue of more than $600 per day from sales of the two items. What combinations of ski and snow board sales will meet or exceed this daily sales goal? Choose two combinations that make sense and explain your choices.
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Homefun Page 303304
#'s 1, 4, 5 (b,f), 6(e), 8, 10
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Exercises: Kuta Worksheets
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