Lesson 3-B
CCSSM Stage 3 Companion Text
Warm-Up
Cody rode his skateboard at a constant speed and then slowed down
as he approached school. The story is shown on the graph below.
Speed
(miles per hour)
1. How fast did Cody ride his skateboard
when he rode at a constant speed?
(0, 8)
(0.5, 8)
8 miles per hour
2. How long did he ride at a constant
speed?
Hours
(0.75, 0)
0.5 hours (30 minutes)
3. How far did he ride at his constant
speed?
4 miles
0.75 hours (45 minutes)
4. What does the point (0.75, 0) mean?
into his ride, Cody
stopped at school.
Lesson 3-B
Direct Variation Tables
and Slope
Vocabulary
Direct Variation
When a graph on a coordinate plane is a straight line that goes
through the origin, it is called a direct variation graph.
In a Table
In Quadrant I
Direct Variation Function
A direct variation graph goes through the origin and
forms a straight line.
The equation for a direct variation function is:
y  mx
 y
where m is the slope, or rate of change   , of the
 x
function.
Example 1
Use the direct variation function y = 3x.
a. Complete the table for the given input values.
b. Draw a scatter plot of the ordered pairs in the table and
connect the ordered pairs with a straight line.
c. Find the slope of the function.
Input, x
0
1
2
3
4
Function Rule
y = 3x
y  3  0  0
y  3 1  3
y  3  2  6
y  3  3  9
y  3  4   12
Output, y
0
3
6
9
12
Example 1 (continued)
Use the direct variation function y = 3x.
b. Draw a scatter plot of the ordered pairs in the table and
connect the ordered pairs with a straight line.
Input, x
0
1
2
3
4
Output, y
0
3
6
9
12
 0,0 
1, 3 
 2,6 
 3,9 
 4,12 
14
12
10
8
6
4
2
1
2 3
4
5
6
7
c. Find the slope of the function.
The slope is the coefficient of the x variable.
y
Also note that  3 for each ordered pair.
x
y  3x
Slope  3
Example 2
Elliot wrote an equation, y = 4.5x, to show the relationship between
the number of days, x, and the total miles, y, he ran. Jacob runs
daily but only recorded his total miles in the table at 2, 5, 10, and 11
days. Who runs more miles, on average, per day?
Elliot JacobTo find Jacob’s unit rate, or
y = 4.5x
slope, find the ratio y to x for
any (x, y) pair from the table:
Days,
x
Total Miles
Run, y
0
0
2
8
Elliot: 4.5 miles per day
5
20
Jacob: 4 miles per day
10
40
11
44
8 miles
 4 miles per day
2 days
Elliot wrote an
equation with a
slope of 4.5. This
slope represents
his daily rate: 4.5
miles per day.
Elliot runs 0.5 more miles
per day than Jacob.
Direct Variation Function
A direct variation graph…
goes through the origin,
forms a straight line,
and has an equation of the form y = mx where m is the
y
slope, or rate of change
, ofthe
 function.
 x
Exit Problems
1. Complete the input-output table and graph the function.
Input
x
Function Rule
y = 2x
Output
y
0
1
2
3
2. The table shows ordered pairs which model direction
variation. Write an equation relating the x and y coordinates.
x
0
1
2
3
4
y
0
3
6
9
12
Communication Prompt
How does direct variation compare to a linear equation
in the form y = mx + b?