PROPORTIONAL AND NONPROPORTIONAL SITUATIONS USING AN EQUATION

Example 1 :

The relationship between the weight of an object on the Moon and its weight on Earth can be represented by the equation y  =  x/6. Is the relationship between the weight of an object on the Moon and its weight on Earth proportional or non-proportional?

Solution :

y = x/6 or y = (1/6)x

The equation is in the form y = mx + b. The value of m is 1/6, and the value of b is 0. Since b is equal to zero, the relationship between the weight of an object on the Moon and its weight on Earth is proportional.

Example 2 :

The number of years since Lenin graduated from middle school can be represented by the equation y = a - 14, where y is the number of years and a is his age. Is the relationship between the number of years since Lenin graduated and his age proportional or non-proportional?

Solution :

y = a - 14

The equation is in the form y = mx + b, with a being used as the variable instead of x. The value of m is 1 and the value of b is -14. Since b is not 0, the relationship between the number of years since Lenin graduated and his age is non-proportional.

Example 3 :

Ken has a weekly goal of burning 2400 calories by taking brisk walks. The equation y = -300x + 2400 represents the number of calories y Ken has left to burn after x hours of walking which burns 300 calories per hour. Is the relationship between the number of hours and calories burned proportional or non-proportional?

Solution :

y = -300x + 2400

The equation is in the form y = mx + b. The value of m is -300, and the value of b is 2400. Since b is not equal to zero, the number of hours and calories burned is non-proportional.

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