(8) Lesson 4.1

1. Course 3, Lesson 4-1
Solve each system of equations algebraically.
1. y = 2x + 3 2. y = x – 6
y = 12 y = 3
3. y = x – 4 4. y = –4x – 8
y = y = –2x
5. Together, Wally and Sam have 20 toy trains. Wally has 8
more trains than Sam. How many trains does each boy
have?
1
3
x

2. ANSWERS
1. (4.5, 12)
2. (9, 3)
3. (6, 2)
4. (–4, 8)
5. Sam has 6 trains and Wally has 14 trains.
Course 3, Lesson 4-1

3. HOW can we model relationships
between quantities?
Functions
Course 3, Lesson 4-1

4. Course 3, Lesson 4-1 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.4
Construct a function to model a linear relationship between two
quantities. Determine the rate of change and initial value of the function
from a description of a relationship or from two (x, y) values, including
reading these from a table or from a graph. Interpret the rate of change
and initial value of a linear function in terms of the situation it models,
and in terms of its graph or a table of values.

5. Course 3, Lesson 4-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council
of Chief State School Officers. All rights reserved.
Functions
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.
5 Use appropriate tools strategically.

6. To
• represent linear relationships using
words, equations, tables, and graphs
Course 3, Lesson 4-1
Functions

7. • linear equation
Course 3, Lesson 4-1
Functions

8. 1
Need Another Example?
2
Step-by-Step Example
1.
Write an equation to find the number
of liters in any number of quarts.
Describe the relationship in words.
Let ℓ represent the liters and q represent the quarts.
The equation is ℓ = 0.95q.
The table shows the number of liters in quarts of liquid.
The rate of change is the rate that
describes how one quantity changes
in relation to another quantity. The
rate of change of quarts to liters
is = or 0.95 liter in
every quart.

9. Answer
Need Another Example?
The table shows the relationship between miles
and kilometers. Write an equation to find the
number of miles in any number of kilometers.
Describe the relationship in words.
m = 0.62k;
There is 0.62 mile in one kilometer

10. 1
Need Another Example?
2
3
4
Step-by-Step Example
2.
There are about 7.6 liters in 8 quarts.
About how many liters are in 8 quarts?
ℓ = 0.95q Write the equation.
ℓ = 0.95(8) Replace q with 8.
ℓ = 7.6 Multiply.

11. Answer
Need Another Example?
The table shows the relationship between miles
and kilometers. Write and use an equation to
find the number of miles in 20 kilometers.
m = 0.62k, 12.4 mi

12. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3.
To find the y-intercept, use the slope and the coordinates of a
point to write the equation of the line in slope-intercept form.
The total distance Marlon ran in one
week is shown in the graph.
Write an equation to find the number of
miles run y after any number of days x.
Find the rate of change or the slope of the line.
Definition of slope
(x1, y1) = (2, 7); (x2, y2) = (4, 14)
Simplify.
Slope-intercept formy = mx + b
Replace m with the slope, 3.5.y = 3.5x + b
Use the point (2, 7). x = 2, y = 77 = 3.5(2) + b
Solve for b.0 = b
The slope is 3.5 and the y-intercept is 0. So, the
equation of the line is y = 3.5x + 0 or y = 3.5x.

13. Answer
Need Another Example?
The total number of miles Suki hiked on certain days
is shown. Write an equation to find the number of
miles hiked after any number of days.
y = 1.5x

14. 1
Need Another Example?
2
3
4
Step-by-Step Example
4. The total distance Marlon ran in one week is shown
in the graph. The equation y = 3.5x represents the
situation. How many miles will Marlon run after 2 weeks?
Write the equation.y = 3.5x
There are 14 days in 2 weeks. Replace x with 14.y = 3.5(14)
Multiply.y = 49
Marlon will run 49 miles in 2 weeks.

15. Answer
Need Another Example?
The total number of miles Suki hiked on certain
days is shown. The equation y = 1.5x represents
the situation. Use the equation to find the
number of miles Suki will hike after 1 week.
y = 1.5x; 10.5 mi

16. Course 3, Lesson 4-1
Functions
Words Distance traveled is equal to 12 miles per second times the
number of seconds.
Equation d = 12s
Table Graph

17. 1
Need Another Example?
2
Step-by-Step Example
5. Chloe competes in jump rope competitions. Her average
rate is 225 jumps per minute.
Let j represent the number of jumps and m represent the minutes.
The equation is j = 225m.
Write an equation to find the number of jumps in any
number of minutes.

18. Answer
Need Another Example?
The average heart rate of a chicken is 275 beats
per minute. Write an equation to find the number
of beats in any number of minutes.
b = 275m

19. 1
Need Another Example?
2
Step-by-Step Example
6. Chloe competes in jump rope competitions. Her average
rate is 225 jumps per minute.
Make a table to find the number of jumps in 1, 2, 3, 4, or
5 minutes. Then graph the ordered pairs.

20. Answer
Need Another Example?
The average heart rate of a chicken is 275 beats
per minute. Make a table to find the number of
beats in 1, 2, 3, 4, or 5 minutes. Then graph the
ordered pairs.

21. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-1
Functions

22. How did what you learned
today help you answer the
HOW can we model relationships
between quantities?
Course 3, Lesson 4-1
Functions
Sample answers:
• An equation can be written using information in a table.
• An equation can be written using information shown in
a graph.
• Linear relationships can be modeled by using words,
equations, tables or graphs.

23. There are 5,280 feet in
every mile. Write an
equation to find the number
of feet f in any number of
miles m. Then find the
number of feet in 2.5 miles.
Ratios and Proportional RelationshipsFunctions
Course 3, Lesson 4-1