A table of values is a list of numbers that are used to substitute one variable, such as within an equation of a line and other functions, to find the value of the other variable, or missing number. The first number chosen to find the second value is called the independent variable, as it is independently chosen for the equation, while the second number, found as the solution of the equation, is the dependent variable. The dependent variable, typically represented by y, relies upon the chosen value of the independent variable, in this case x.
Equation of a Line
A table of values is used to graph a line according to its equation, and it is also used to find the specific equation of a graphed line, from finding the coordinates of some of its points and plugging the values into the standard formula, y = mx + b. With any given equation, values are usually listed as x and y values. The x value is plugged into the equation, in place of x, then the equation is solved for y. The answer is then entered into the table of values under the y column, next to its coordinating x value--the one that yielded the y solution. These numbers are listed in the same row because the table of values lists the relationship between the x and y numbers.
Functions also use a set of ordered pairs--pairs that are arranged in the order of the x coordinate, then the y coordinate--where the chosen values of x yield only one value for y, when the x number is substituted in the problem. If the x value produces more than one value for y, then the problem is not a function. The values that result from the first variable are described as "the function of." For example, if the table of values uses numbers for x that will find y, then the y numbers are described as a function of x, or f(x), since the x values resulted in the y numbers listed.
Unique to Each Equation
Each equation has its own table of values by which the first column is used to find the second column. All of the resulting numbers answer the statement of the equation, such that y is equal to the value of x's calculation in the equation.
Once the table of values is completed, it is a simplified process to pull out the ordered pairs of (x,y) values. Simply take the x value from the first line and write it after the opening parenthesis. Next, add a comma, then write the y number from the first line, and close the parenthesis.
Graphing a line from a table of values is not difficult. With just two coordinated pairs, (x,y) values that represent points on the line, the line can be drawn out and extended along its path, beyond the two graphed points.