The expression 'y/x = k' represents a relationship where the ratio of two variables, y and x, is equal to a constant value, k. This relationship is known as a direct variation, and it is a fundamental concept in the study of functions and their properties.
congrats on reading the definition of y/x = k. now let's actually learn it.
The expression 'y/x = k' indicates that the ratio of the two variables, y and x, is constant and equal to the value of k.
The constant of proportionality, k, determines the rate of change between the two variables, y and x, in a direct variation relationship.
In a direct variation relationship, as one variable increases, the other variable increases proportionally, and vice versa.
Direct variation relationships are often used to model real-world situations, such as the relationship between the cost of an item and the quantity purchased.
The expression 'y/x = k' can be rearranged to 'y = kx', which is the standard form of a direct variation equation.
Review Questions
Explain how the expression 'y/x = k' represents a direct variation relationship between the variables y and x.
The expression 'y/x = k' indicates that the ratio of the two variables, y and x, is constant and equal to the value of k. This means that as one variable (x) increases, the other variable (y) increases proportionally, and vice versa. The constant of proportionality, k, determines the rate of change between the two variables in a direct variation relationship. This type of relationship is often used to model real-world situations where one variable is directly proportional to another, such as the relationship between the cost of an item and the quantity purchased.
Describe how the expression 'y/x = k' can be rearranged to the standard form of a direct variation equation, 'y = kx'.
The expression 'y/x = k' can be rearranged to the standard form of a direct variation equation, 'y = kx', by multiplying both sides of the equation by x. This manipulation allows the constant of proportionality, k, to be isolated and expressed as the coefficient of the variable x. The standard form 'y = kx' is useful for representing direct variation relationships in a more familiar linear equation format, which can be used to make predictions, calculate values, and analyze the relationship between the two variables.
Analyze how the concept of 'y/x = k' can be applied to real-world situations to model and understand the relationship between two variables.
The expression 'y/x = k' can be applied to a wide range of real-world situations to model and understand the relationship between two variables. For example, in the context of economics, the relationship between the cost of an item and the quantity purchased can be represented using the direct variation expression 'y/x = k', where y represents the cost and x represents the quantity. This model can be used to analyze the rate of change, or the constant of proportionality, between the two variables and make predictions about how changes in one variable will affect the other. Similarly, in the field of physics, the expression 'y/x = k' can be used to model the relationship between variables such as velocity and time, or force and acceleration, allowing for a deeper understanding of the underlying principles governing these relationships.
A relationship between two variables where one variable is proportional to the other, meaning that as one variable increases, the other variable increases proportionally.
Inverse Variation: A relationship between two variables where one variable is inversely proportional to the other, meaning that as one variable increases, the other variable decreases proportionally.
The value 'k' in the expression 'y/x = k' that represents the constant of proportionality, which determines the rate of change between the two variables.