## Unit 3:

## Graphing Equations & Inequalities

### Unit 3 - Graphing Equations & Inequalities

**Learning Targets/Performance Indicators**

- Choose and interpret the scale and the origin in graphs and data displays.
- Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane.
- Graph the solutions to a linear inequality in two variables as a half-plane.
- Choose an appropriate graphing technique based on the form of the equation or inequality (i.e., standard form, slope-intercept form, point slope form).
- Choose an appropriate graphing technique based on the context of a given situation.
- Write equations of lines that are parallel or perpendicular to a given line and passing through a given point.

**Essential Questions:**

- How can you use linear equations and inequalities to model a real-world situation?
- What are the differences and similarities between the solution set of an inequality versus the solution set of an equation?
- What are the different methods used to graph an equation and an inequality; in what equation form is each method most appropriate?

**Prior Learning:**

In grade 6, students used variables to represent two quantities and identified independent and dependent relationships in graphs, tables, and equations. (6.EE.9)

In grade 7, students analyzed proportional relationships and identified constants of proportionality in tables, graphs, equations, diagrams, and verbal descriptions. (7.RP.2) Students explained what a point on the graph meant in terms of a situation.

In grade 8, students identified equations of the form y = mx + b as linear functions whose graphs are a straight line, and they identified functions that are not linear (e.g., A = s2).

- (8.F.3) Students defined a function (not using function notation) and created function tables to generate ordered pairs as a means of graphing a function. Students determined rate of change and represented it in multiple ways.
- (8.F.4) Students graphed proportional relationships and interpreted the unit rate as the slope of the graph.
- (8.EE.5) They used similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line and derived the equation y = mx + b.
- (8.EE.6) In previous units, students created expressions and equations, and they solved equations in one variable.

**Current Learning:**

Students deepen their knowledge of graphing and expand their understanding of linear and non-linear equations and their graphs. Students graph equations and inequalities from multiple forms including slope-intercept form, standard form, and point-slope form. They explore the graphs of non-linear equations and inequalities and determine the difference between equations and inequalities that are linear vs. non-linear. Students choose and interpret an appropriate scale and the origin in graphs and data displays.

**Future Learning:**

Students will use the knowledge gained in this unit to investigate and solve systems of linear equations and to support their further study of the graphs of more complex functions. Students will also use the material learned in this unit when they fit a linear function to a given set of data. They will continue to build on these concepts in subsequent mathematics courses.