Linear Relationships: Graphs

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

Linear Equation


Y=mx + b is the format of equations that are linear. The m represents the slope. The b represents the y-intercept. The x and y-values are represented by x and y where the numbers are changing but are changing in a way that is constant.

Linear Relationships in Graphs

Linear relationships in graphs are easy to recognize. If a graph is a straight line, then it is linear. The relationship that is graphed can be determined by the direction and steepness of the graph. The steepness and direction is represented by a number. The direction is based on whether the steepness is positive and negative. The larger the value the more steep the graph. The relationship can be determined where the graph crosses the y-axis (y-intercept) as well. The slope (direction and steepness of the graph) and the y-intercept will tell use about the relationship that is being graphed.

The Y-Intercept

The y-intercept in the graph is determined by where the graph crosses the y-axis. This point usually represents where the relationship between the x-value and the y-value begins.

The Slope

The slope in the graph is the steepness and direction of the line. We read graphs left to right. If it appears that the graph is moving up then the slope is positive. If it appears the graph is moving down then the slope is negative. If the graph is straight up and down then there is no slope. If the graph is perfectly horizontal, then the slope is undefined. The more steep the graph the higher the digits will be that represents the slope.

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Linear Relationships in Tables


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