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How to Determine a Linear Relationship

A linear relationship refers to a relationship between two variables where the dependent variable increases or decreases by a set amount each time the independent variable changes. For example, if you make horseshoes at a rate of 10 per hour, the independent variable is time elapsed and the dependent variable is the number of horseshoes produced. As time elapsed increases by one hour, the number of horseshoes produced increases by 10. Knowing the linear relationship helps you predict future performances. In this example, you could predict how many horseshoes could be created in a day, week, or an even longer period of time.

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Instructions

    • 1

      Subtract the starting value of the independent variable from the ending value of the independent variable. For example, if you want to find the linear relationship between horseshoes made and time elapsed, time elapsed would be the independent variable. If you started at zero and worked for five hours, subtract zero from five to get five.

    • 2

      Subtract the starting value of the dependent variable from the ending value of the dependent variable. In this example, horseshoes made is the dependent variable. If you started with 10 horseshoes and ended with 60 horseshoes, subtract 10 from 60 to get 50.

    • 3

      Divide the change in the dependent variable by the change in the independent variable to find the slope of the linear relationship. In this example, divide 50 by 5 to find that the slope equals 10.

    • 4

      Plug in the slope and one of the coordinate pairs to find the y-intercept, b, in the following equation: y = mx+b, where m is the slope. In this example, plug in 5 for x, 60 for y, and 10 for x to find 60 = 50 + b, meaning b = 10.

    • 5

      Plug in the slope and the y-intercept to complete the linear equation in the form y = mx +b. Completing the example, plug in 10 for m and 10 for b to find that the equation equals y = 10x + b.

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