WEEK 4-GRAPHING-TWO-VARIABLE-INEQUALITIES

Graphing Two-Variable Inequalities

Objectives

Start

Two-Variable Inequalities

Graphing Inequalities

From Words to Inequalities

Geogebra Practice

Summary

Two-Variable Inequalities

What are 2 variable Linear Inequalities?

Definition: A linear inequality is in any of the following forms:ax+by+c>0, ax+by+c<0, ax+by+c≥0, ax+by+c≤0

Here:

Example 1: 3x + 4y ≥1 is a linear inequality which means: "Three times a number added with four times another number is greater than or equals to one".

x and y

are variables

are constants.

a, b, and c

Try it by yourself:

Graphing Inequalities

All possible solutions of an inequality are inside a region of XY plane.

Example: Graph the solution set of 2x+y≤3 .

Step 4

Step 1

Step 3

Step 2

If x raises 1 unit y decreases by 2.

m=-2

y-intercept is in x=0, y=3.

b=3

Let's see some examples:

Example 2: Graph the solution set of x<2.

Example 1: Graph the solution set of y≥1.

From Words to Inequalities

Let's see some examples:

Example 1: "Three times a number minus the double of another number is greater than 50". Write an inequality of the situation.

Example 2: A bakery spends 10 min baking a bread and 3 minutes a cookie. If the bakery is able to produce at most for 9 hours, write an inequality of the situation

3x-2y>50

10b+3c≤540

Try it by yourself:

Geogebra Practice

Imagine that you set aside $50 in your budget for books ($5 each) and notebooks ($2 each).

The task is to determine the possible combinations of books and notebooks to buy.

Cost of books: $5 ∙📖 Cost of notebooks:$2∙📔 Total: $5 ∙📖+$2∙📔

Now, let: x = books, y = notebooks, then, the inequality becomes:5x+2y≤50

Now, let's see the results on Geogebra:

Take in mind that x and y should be greater than or equals to zero.

Summary: Graphing an Inequality

SOLVE FOR Y

IF

GREATER THAN OR EQUALS TOy≥...

GREATER THAN y>...

LESS THAN OR EQUALS TOy≤...

LESS THAN y<...

Great job!

See you next time

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MA.912.AR.2: Write, solve and graph linear equations, functions and inequalities in one and two variables. MA.912.AR.2.7 Write two-variable linear inequalities to represent relationships between quantities from a graph or a written description within a mathematical or real-world context. MA.912.AR.2.8 Given a mathematical or real-world context, graph the solution set to a two-variable linear inequality.

MATERIAL

It is highly advised to have:

• Grid paper.
• Pencils of different colors.
• Eraser.
• A rule.
• A calculator.
• Geogebra installed on your phone/tablet/computer (or use online version).