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

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.

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

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.

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.

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

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

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

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

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 = -18 + b 18 + 4 = -18 + 18 + b 22 = b Hey, that is the same b we found in the table of values.

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

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