Linear relationships can be expressed as equations, graphs, and tables. This post looks closer at linear relationships expressed in tables.
With linear equations, we use the format y-mx+b where m is the slope and the b is the y-intercept. The equation if graphed would create a straight line graph. The x and y values of ordered pairs would create and be a part of a straight line. When written as an equation, we leave the variables of x and y in the equation. The y-values usually represents some type of total, and the x represents a number of some kind.
Linear Relationships in Tables
Linear relationships can be represented in equations and graphs. In addition, linear relationships can be represented in a table of values. Linear tables usually have two sets of values, a set of values represented by “x” and a set of values represented by “y”. The x’s are a number of something and the y’s usually totals. The tables can either be vertical or horizontal. The vertical tables have the x-values, called inputs, on the left column and the y-values, called outputs, on the right column. The horizontal tables have the x-values on the top row and the bottom row contains the y-values. Tables are linear when the x-values and y-values express a constant rate of change. The relationship expressed in the table can be put into an equation or graphed once the constant rate of change (slope) and y-intercept are determined.
The Y Intercept
The y-intercept is the value of y when the x value is equal to zero. Sometimes, the y-value is zero when the x value is zero so the table may not show an actual y-intercept. It is where the graph of the relationship passes the y-axis when graphed. This would indicate that the relationship expressed in the table is linear and proportional.
The Slope (rate of change)
The slope or rate of change is the relationship between how the x values change as the y-values change. The slope is determined by dividing the change of y values by the change of x values. It is the steepness and direction of the graph. Once the slope and y-intercept are determined an equation can be written to represent the table and the relationship can be graphed (if it is linear, the graph will be a straight line).