# Write an equation for the linear function represented by the table

A table of values is a graphic organizer or chart that helps you determine two or more points that can be used to create your graph. Why Use a Table of Values? In order to graph a line, you must have two points. For any given linear equation, there are an infinite number of solutions or points on that line. Opening 10 minutes I begin class today by writing a linear equation on the board. I ask students, based on what they have learned so far in this unit, about different ways they can represent this equation. I want to elicit from students that they could graph it, represent it tabularly, or write a real world situation to describe the equation.

Next, I put up a table of values that also represents a linear function.

## MAT Linear Relationships: A Review

Again, I ask students different ways they could represent the data in the table. Students will likely begin to see the point I am trying to make: I ask them about the characteristics of linear functions. What makes them linear? I want to be sure students hit on both the idea of a rate of change and a starting point.

I ask them again, where they can see these characteristics in the equation I started class with. I tell students that today they will be working in groups to write a guide about how to move from one representation to another.

I might assign, or let groups choose a starting point and then ask them to write instructions for all of the conversions from that starting representation.

## Linear Functions Word Problems

For example, one group might be assigned the starting point Situations. This group must write instructions for how to go from a Situation to a Graph, a Situation to a Table, and a Situation to an Equation. I ask each group to make a poster that they will eventually present to the class. It sometimes helps students to tell them to imagine they are writing a guide for future students who have yet to take this class.

This places students in the role of "expert" and can help them with the tone of their writing. Depending on my class, I might think through the groups of students and assignments of a starting point before class especially if I want certain groups to work on areas they struggle with or with more challenging conversions.Linear Functions Make this Foldable to help you organize your notes.

Begin with seven sheets of linear function (p. ) slope (p. ) Real-World Link data (such as a table, graph, equation, or verbal description). The student uses graphs, tables, and algebraic representations to. A linear function can be described by a linear equation.

A linear equation is a degree-1 polynomial. In other words, each term in a linear equation is either a constant or the product of .

The general formula for a linear function is represented by the equation y=mx+b. This type of equation is set in slope-intercept form, which is the most common form you will see.

Next, I put up a table of values (that also represents a linear function). Again, I ask students different ways they could represent the data in the table.

## The Absolute Value Function

Students will likely begin to see the point I am trying to make: linear functions can be represented as tables, equations, graphs, and situations.

A function table in math is a table that describes a function by displaying inputs and corresponding outputs in tabular form. Each function table has a rule that describes the relationship between.

Writing Equation from Table of Values. Often, students are asked to Write the equation of a line from a table of values. To solve this kind of problem, simply chose any 2 points on the table and follow the normal steps for writing the equation of a line from 2 points.

Piecewise Functions