Notes 4.2.2013
Name:
8th Grade Math
Date:
Advisory:
SWBAT determine the rule of a linear function from a table of values and use that rule to write an
algebraic equation to model the table of values and identify any value of the function.
Think About It!
Directions: Look at the table below and explain the pattern. Be sure to explain where the pattern starts
and how much it increases or decreases.
𝒙
𝒚
Pattern:
0
3
1
4
2
5
3
6
4
7
5
8
Vocabulary
1. Linear Function – A function whose outputs (𝑦-values) increase/decrease by a
rate as the inputs (𝑥-values) increase.
Example #1: Identifying the Relationship Between 𝑥 and 𝑦
Directions: Use the table to identify the patterns for the 𝑥 and 𝑦 values. Determine what is
happening to each 𝑥 to result in each corresponding 𝑦.
𝒙
𝒚
0
3
What is the relationship?
1
4
2
5
3
6
4
7
Relationship as Algebraic Rule:
5
8
What if there is more than ONE operation between 𝑥 and 𝑦? Let’s consider the table below.
Operations 𝒚
𝒙
If we cannot add or multiply each 𝑥 by the same amount to result in each
0
1
corresponding 𝑦, then there must be two operations being applied to each 𝑥.
1
4
2
7
If 𝑦 ≠ 0 when 𝑥 = 0, the algebraic rule must include
3
10
or
.
4
13
5
16
Relationship as Algebraic Rule:
Partner Work
Directions: Use the tables to identify the patterns for the 𝑥 and 𝑦 values. Determine what is
happening to each 𝑥 to result in each corresponding 𝑦. Decide how many operations are being applied
to each 𝑥 to result in each corresponding 𝑦. Write the verbal rule and translate it into the algebraic rule.
𝒙
Operations
𝒚
0
0
1
2
2
4
3
6
4
8
5
10
𝒙
Operations
𝒚
0
2
1
4
2
6
3
8
4
10
5
12
𝒙
Operations
𝒚
0
-1
1
0
2
1
3
2
4
3
5
4
Number of Operations:
Verbal Rule:
Algebraic Rule:
Number of Operations:
Verbal Rule:
Algebraic Rule:
Number of Operations:
Verbal Rule:
Algebraic Rule:
Example #2: Applying the Algebraic Rule to Extend the Table of Values
Number of Operations:
𝒙
Operations
𝒚
1
1
2
3
3
5
4
7
5
9
Verbal Rule:
Algebraic Rule:
Use the algebraic rule to find missing 𝑦-values for the coordinate pairs below. Show your work.
a. (10,
)
b. (100,
)
c. (250,
)
Partner Work
Directions: Determine the algebraic rule for each table then use that rule to find the missing
values in the tables.
𝒙
Operations
𝒚
0
0
1
-1
2
-2
3
-3
4
-4
5
-5
10
Number of Operations:
Verbal Rule:
Algebraic Rule:
100
Would the points above form a line in the coordinate plane? Explain your reasoning.
Operations
𝒙
𝒚
1
-1
2
0
3
1
4
2
5
3
Number of Operations:
Verbal Rule:
10
Algebraic Rule:
100
Explain the steps you had to take to determine the algebraic rule for the table.
Independent Practice
Directions: Write the algebraic rule for each table and use the rule to find the missing values.
𝒙
𝒚
2
10
3
15
4
20
5
25
10
50
Algebraic Rule:
𝒙
0
1
2
3
4
10
30
𝒚
-1
2
5
8
11
Algebraic Rule:
Directions: Match the correct algebraic rule to its corresponding table of values. Make sure that
you are thinking about whether the 𝑦-values are increasing or decreasing.
a. 𝑦 = 4𝑥
𝒙
-2
-1
0
1
b. 𝑦 = 𝑥 − 4
𝒚
-6
-5
-4
-3
Rule:
𝒙
-3
-2
-1
0
c. 𝑦 = −𝑥 − 4
𝒚
-12
-8
-4
0
Rule:
𝒙
-1
0
1
2
𝒚
-3
-4
-5
-6
Rule:
Directions: Write an algebraic rule for each table below. Then use that rule to find each missing
𝑦-value for the given 𝑥-values.
𝒙
1
2
3
4
20
Rule:
Show your work.
𝒚
0.5
1.5
2.5
3.5
𝒙
1
2
3
4
100
Rule:
𝒚
0.5
1
1.5
2
𝒙
1
2
3
4
30
Rule:
𝒚
2.5
5
7.5
10
Exit Ticket 4.2.2013
Name:
8th Grade Math
Date:
Advisory:
Directions: Write an algebraic rule for each of the tables below.
𝒙
-1
0
1
2
𝒚
-1
0
1
2
𝒙
-1
0
1
2
Rule:
Rule:
𝒚
-3
-2
-1
0
𝒙
1
2
3
4
𝒚
5
9
13
17
Rule:
Directions: Write an algebraic rule for the table below, then use the rule to find the missing 𝑦-values.
𝒙
0
1
2
3
10
100
𝒚
1
3
5
7
Show your work
Rule:
How did you apply the algebraic rule you determined to find the value of 𝑦 when 𝑥 = 100? Explain.