#### Lesson Plan

## Two-Variable Equations and Inequalities

### Alignments:

### Grade Levels

### Related Academic Standards

### Assessment Anchors

### Eligible Content

### Big Ideas

### Concepts

### Competencies

### Objectives

Students will understand the connection between equations and slope-intercept form and solve/graph two-variable equations and inequalities. They will:

- represent real-world scenarios with two-variable equations and inequalities.
- find solutions to two-variable equations and inequalities.
- write an equation in slope-intercept form.
- solve a two-variable equation for one variable.
- solve a two-variable inequality for one variable.
- graph two-variable linear equations and inequalities.

### Essential Questions

- How can mathematics support effective communication?
- How are relationships represented mathematically?
- How can expressions, equations and inequalities, be used to quantify, solve, model, and/or analyze mathematical situations?
- How can data be organized and represented to provide insight into the relationship between quantities?

### Vocabulary

**Coefficient:**The coefficient of a term in an expression is the number that is multiplied by one or more variables or powers of variables in the term.**Function:**A relation in which every input value has a unique output value.**Linear Equation:**An equation of the form*A*+*x**B*=*y**C*, where*A*≠ 0 and*B*≠ 0. The graph of a linear equation is a straight line.**Rate of****Change:**The ratio of the change in the output value and change in the input value of a function.**Simultaneous Linear Equations:**Two or more linear equations that share a set of variables and either exactly one solution, no solutions, or infinitely many solutions; often called a “system of equations.”**Slope:**The measure of the steepness of a line; the ratio of the change in the*y*-values to the*x*-values of the linear function; rate of change.The*y*-intercept:*y*-coordinate of the point where a line intersects the*y*-axis; the value of the function when*x*= 0.

### Duration

90–120 minutes

### Prerequisite Skills

### Materials

- Memory Cards (M-8-2-3_Memory Cards.docx)
- Entrance Ticket (M-8-2-3_Entrance Ticket.doc)
- Graphing Inequalities (M-8-2-3_Graphing Inequalities.docx and M-8-2-3_Graphing Inequalities KEY.docx)
- Systems of Inequalities (M-8-2-3_Systems Extension.docx and M-8-2-3_Systems Extension KEY.docx)
- envelopes

### Related Unit and Lesson Plans

### Related Materials & Resources

The possible inclusion of commercial websites below is not an implied endorsement of their products, which are not free, and are not required for this lesson plan.

- http://www.purplemath.com/modules/solvelit.htm
- http://www.purplemath.com/modules/graphlin.htm
- http://www.purplemath.com/modules/ineqgrph.htm

### Formative Assessment

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