1. Creating a Table of Values April 12th, 2011
Journal Entry
Creating a Table of Values
April 12th, 2011

2. What is a table of values?
A table of values shows the relationship between the independent variable (x),domain, and dependent variable (y), range, given by an equation. Any value of x c(an be used to find the associated y using the equation.

3. Typical Table of Values
The x-values used in most table of values is:
x y = EQUATION (x, y) -2 -1 1 2

4. When you are given an equation:
Given the following equation, make a table of values:
y = 2x - 3 x y
(x, y) -2
2(-2) – 3 = -7
(-2, -7) -1
2(-1) – 3 = -5
(-1, -5)
2(0) – 3 = -3
(0, -3) 1
2(1) – 3 = -1
(1, -1) 2
2(2) – 3 = 1
(2, 1)
Remember, the equation stays the same each time and the value in the bracket is the value in the x column.
The coordinates are the number in the x column and the value found for y.

5. Using the Table of Values for the graph:
Each of the coordinates found in the table of values represents a point on the line.
We really only need two of the points to find the line but ensure all of the points fall on the line.
Note the relationship between x and y. The value of y is twice the value of x, minus 3. Exactly as the equation y = 2x – 3 describes.

6. Graph: y
(1, 1)
(1, -1)
(0, -3)
(-1, -5)
(-2, -7) x
y = 2x - 3

7. Getting the equation from a table of values:
When you are given a table of values you can find the equation. x y -2 15 -1 22 29 1 36 2 43
To find the slope (m), you must determine the “jump” between the values in the y-column (as long as the x values are going up by 1).
To find the y-intercept (b), look at the y-value when the x-value is zero.
Therefore the equation representing this table of values is
y = 7x + 29 7 7 7 7

8. What happens there is no x-value of zero in the table of values?
You must look for a pattern and either extend the table of values OR find the y-intercept algebraically OR you can graph the table of values.
I still look at the jump to determine the slope (m).
So m = -6. x y 3 4 -2 5 -8 6
-14 7
-20

9. Now the y-intercept: x y 22 1 16 2 10 3 4 -2 5 -8 6 -14 7 -20
Extending the table:
Just continue the pattern (backwards in this case) until you reach the point you need.
So b = 22. x y 22 1 16 2 10 3 4 -2 5 -8 6
-14 7
-20

10. Hey, that is the same b we found in the table of values.
Another Way:
Algebraically:
I know the slope is -6 (m = -6), and I want to find the value of b.
Pick a pair of values from the table. Put the x and y in the equation (y = mx + b) and solve for b.
(3, 4) ~ so x = 3, y = 4
y = mx + b
4 = -6(3) + b
4 = b
= b
22 = b
Hey, that is the same b we found in the table of values.

11. Yet another way: Graphically 24 20 16 12 8
The line crosses the y axis at 22, therefore the y-intercept is 22.
So b = 22. 4 x -4 -8
-12
-16
-20 y

12. The Equation
It didn’t matter which method was used, the y-intercept was 22.
So we know from the table that the slope (m) was -6 and all methods showed the y-intercept (b) was 22.
y = -6x + 22