Linear relationships can be expressed as equations, graphs, and tables. This post looks closer at linear relationships expressed in tables.

## Linear Equation

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).

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