Graphs of Linear Functions and Rate of Change
Video solutions to help Grade 8 students examine and recognize real-world functions with discrete rates and continuous rates.
Plans and Worksheets for Grade 8
Plans and Worksheets for all Grades
Lessons for Grade 8
Common Core For Grade 8
New York State Common Core Math Module 5, Grade 8, Lesson 6
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
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
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.
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.
• 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.