Graphs of Linear Functions and Rate of Change

Examples, videos, and solutions to help Grade 8 students examine and recognize real-world functions with discrete rates and continuous rates.

New York State Common Core Math Grade 8, Module 5, Lesson 6

Worksheets for Grade 8

Lesson 6 Student Outcomes

• Students know that the definition of a graph of a function is the set of ordered pairs consisting of an input and the corresponding output.
  
• Students understand why the graph of a function is identical to the graph of a certain equation.

Lesson 6 Student Summary

When the rate of change is constant for pairs of inputs and their corresponding outputs, the function is a linear function.
We can write linear equations in the form of y = mx + b to express a linear function.
From the last lesson we know that the graph of a function is the same as the graph of the equation that describes it. When a function can be described by the linear equation y = mx + b, the graph of the function will be a line because the graph of the equation y = mx + b is a line.

Lesson 6 Classwork

Opening Exercise
Functions 1, 2, and 3 have the tables shown below. Examine each of them and make a conjecture about which will be linear and justify your claim.
Exercise
A function assigns the inputs and corresponding outputs shown in the table below.
a. Is the function a linear function? Check at least three pairs of inputs and their corresponding outputs.
b. What equation describes the function?
c. What will the graph of the function look like? Explain.

Closing

• We know that if the rate of change for pairs of inputs and corresponding outputs is the same for each pair, the function is a linear function.
  
• We know that we can write linear equations in the form of to express a linear function.
  
• We know that the graph of a linear function in the form of will graph as a line because all equations of that form graph as lines. Therefore, if a function can be expressed in the form of , the function will graph as a line.

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