6.1 - Relations and Table of Values
Warm Up: Evaluate the following:
4
1
a) 3 (3)
b) 2 (4)
c)
2
(9)
3
3
d) − 2 (12)
4
e) − 5 (10)
A ___________________ is a set of ordered pairs; values of the independent variable, ___, are paired
with values of the dependent variable, ___.
A _____________________ ______ _______________________ is a list of independent values and
the corresponding dependent values.
How to “effectively” create a Table of Values
Example:
𝒚 = 𝟐𝒙 − 𝟏
x
y
Create a good “range” of x values.
 Usually zero in the middle.
 Negative values above.
Positive values below
Make x values multiples of the x-term’s
coefficient’s denominator
Like a number line.
calculations
To get your y values, substitute
chosen x values into the
equation
Graphing with a Table of Values
Example 1: Make a table of values and graph the relation 𝑦 = 3𝑥 + 2.
x
y
Calculations
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
x
2
4
6
8
10
-4
-6
-8
-10
Example 2: Graph the line 𝑦 = −2𝑥 + 2 using a table of values.
x
y
Calculations
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
-4
-6
-8
-10
x
2
4
6
8
10
Example 3: Graph the line y  
3
x  3 using a table of values.
2
(Use multiples of denominator as x-values)
x
y
Calculations
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
x
2
4
6
8
10
-4
-6
-8
-10
3
4
Example 4: Graph the line 𝑦 = 𝑥 − 3 using a table of values.
x
y
10 y
Calculations
8
6
4
2
-10
-8
-6
-4
-2
-2
-4
-6
-8
-10
x
2
4
6
8
10
Graphing with a Table of Values - Practice
Make a table of values and graph the following relations:
1) y 
2
x
3
2) y  3
10 y
3) y  3x  4
x
y
x
y
x
y
8
6
4
2
-10
-8
-6
-4
-2
x
2
-2
4
6
8
10
-4
-6
-8
-10
10 y
8
6
4
2
-10
-8
-6
-4
-2
x
2
-2
4
6
8
10
-4
-6
-8
-10
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
-4
-6
-8
-10
x
2
4
6
8
10
Graphing with a Table of Values - Practice
4) y  
1
x 2
4
5) y  5x  2
10 y
6) y  
x
y
x
y
x
y
8
6
4
2
-10
-8
-6
-4
-2
-2
x
2
4
6
8
10
-4
-6
-8
-10
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
x
2
4
6
8
10
-4
-6
-8
-10
10 y
8
6
4
2
-10
-8
-6
-4
-2
-2
-4
-6
-8
-10
x
2
4
6
8
10
cont’d…
3
x5
4