(8) Lesson 4.7

1. Course 3, Lesson 4-7
Write an equation in y = mx + b form for each function.
1.
2.
3. The table shows the relationship between time and the water level
in a fish tank. What was the initial amount of water in the fish tank?
Assume the relationship between the two quantities is linear.

2. Course 3, Lesson 4-7
ANSWERS
1.
2.
3. 12 inches
1 1
2
2 2
 y x
3 5 y x

3. HOW can we model relationships
between quantities?
Functions
Course 3, Lesson 4-7

4. Course 3, Lesson 4-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Functions
• 8.F.1
Understand that a function is a rule that assigns to each input
exactly one output. The graph of a function is the set of ordered
pairs consisting of an input and the corresponding output.
• 8.F.3
Interpret the equation y = mx + b as defining a linear function,
whose graph is a straight line.

5. Course 3, Lesson 4-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Functions
• 8.F.5
Describe qualitatively the functional relationship between two
quantities by analyzing a graph (e.g., where the function is
increasing or decreasing, linear or nonlinear). Sketch a graph that
exhibits the qualitative features of a function that has been
described verbally.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
7 Look for and make use of structure.

6. To
• identify linear and non linear
functions
Course 3, Lesson 4-7
Functions

7. • nonlinear function
Course 3, Lesson 4-7
Functions

8. 1
Need Another Example?
2
Step-by-Step Example
1. Determine whether the table represents
a linear or nonlinear function. Explain.
As x increases by 2,
y decreases by 15 each time.
The rate of change is constant,
so this function is linear.

9. Answer
Need Another Example?
Determine whether the table
represents a linear or nonlinear
function. Explain.
Nonlinear; the rate of change is not constant.

10. 1
Need Another Example?
2
3
Step-by-Step Example
2. Determine whether the table represents
a linear or nonlinear function. Explain.
As x increases by 3, y increases
by a greater amount each time.
The rate of change is not a constant,
so this function is nonlinear.
Graph the points on a coordinate plane.
Check
The points do not fall in a line. The function is nonlinear.

11. Answer
Need Another Example?
Determine whether the table
represents a linear or nonlinear
function. Explain.
Linear; the rate of change is constant,
as x increases by 3, y increases by 9.

12. 1
Need Another Example?
2
3
4
Step-by-Step Example
3. Use the table to determine whether the minimum
number of Calories a tiger cub should eat is a
linear function of its age in weeks.
Use the table to find the rates of
change.
1,000 – 825 = 175
The rates of change are not the same. Therefore, this
function is nonlinear.
Check Graph the data to verify the ordered pairs do not lie on a
straight line.
1,185 – 1,000 = 185
1,320 – 1,185 = 135
1,420 – 1,320 = 100

13. Answer
Need Another Example?
Use the table below to determine whether or
not the number of revolutions per hour of a
second hand on a clock is a linear function of
the number of hours that pass.
Linear function; the rate of change is constant;
as the number of hours increases by 1, the
number of second hand revolutions increases
by 60.

14. 1
Need Another Example?
2
Step-by-Step Example
4. A square has a side length of s inches. The area of
the square is a function of the side length. Does this
situation represent a linear or nonlinear function?
Explain.
Make a table to show the area of the square for side
lengths of 1, 2, 3, 4, and 5 inches.
Graph the function. The function
is not linear because the points
(1, 1), (2, 4), (3, 9), (4, 16), and
(5, 25) are not on a straight line.

15. Answer
Need Another Example?
At the first level of a maze, there are three possible
paths that can be chosen. At the next level, each of
those three paths have three more possible paths.
Does this situation represent a linear or nonlinear
function? Explain.
Nonlinear; if you graph the function
the points do not lie on a straight line.

16. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-7
Functions

17. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-7
Functions
Sample answers:
• In a function, if the rate of change between any two
data points is a constant, the function is linear.
• In a function, if the rate of change between any two
data points is not a constant, the function is nonlinear.

18. Explain how to tell whether
a table of x-values and
y-values describes a
function.
Ratios and Proportional RelationshipsFunctions
Course 3, Lesson 4-7