**Proportional and nonproportional situations using an equation :**

If a relationship is nonlinear, it is nonproportional. If it is linear, it may be either proportional or nonproportional. When the graph of the linear relationship contains the origin, the relationship is proportional.

Linear equations can be written in the form y = mx + b. When b ≠ 0, the relationship between x and y is non proportional.

**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 nonproportional ?

**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 nonproportional ?

**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 nonproportional

**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 nonproportional ?

**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 nonproportional.

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