Here are the essential concepts you must grasp in order to answer the question correctly.
Direct Variation
Direct variation describes a relationship between two variables where one variable is a constant multiple of the other. If y varies directly as x, it can be expressed as y = kx, where k is a non-zero constant. This means that as x changes, y changes in a proportional manner.
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Proportional Relationships
In a proportional relationship, the ratio of the two variables remains constant. For example, if y varies directly as x, then the ratio y/x = k remains the same regardless of the values of x and y. This concept is crucial for understanding how changes in one variable affect the other in direct variation.
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Effect of Halving x
When x is halved in a direct variation scenario, the value of y will also be halved. This is because if x is reduced to x/2, substituting this into the direct variation equation y = kx results in y = k(x/2) = (k/2)(x), demonstrating that y is directly proportional to x and will change accordingly.
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