Linear Relationships: Situations

Linear Relationships can be expressed in graphs, tables, and equations. In this post, we look at linear relationships in real world situations.

Linear Equation

Any linear relationship can be expressed with this equation, y-mx+b. Y usually represents a total that can change based on the value of the x. X represents the number of something that can affect the y-value. The m represents the slope or rate of change. The b represents the y-intercept or starting value(s) in a linear relationship.

Linear Relationships in Real-World Situations

Linear relationships refer to real-world quantitative relationships in which the value of one thing directly affects the value of another thing. Sometimes this is referred to as direct variation depending on the starting value of the relationship. The relation always contains a rate. If the relationship starts with the total (y) of zero when the x-value starts with zero, then the relationship is proportional. Otherwise, the relationship is non-proportional. The slope (m) is a rate and can usually be identified in a real-world problem with words such as ‘per, each, and every.” The y-intercept (b) can usually be identified by words such as “fee, starting amount, initial value…”The x-value is considered an independent variable. The y-value is considered a dependent variable. So, whatever y represents is dependent of whatever x represents.

The Y-Intercept

The y-intercept is where a linear graph crosses the y-axis. It is what the value of y is when x is zero. In a situation. It can be identified by words such as “initial value, fee, starting amount, one-time charge, and so on…).

The Slope

The slope is the direction and steepness of a linear (straight line) graph. In a table, it can be identified by dividing the change of y by the change of x. In a real-world situation, it can be identified by words such as “per, each, and every.”

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Linear Relationships in Tables

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