Final answer:
The equation y = k/x represents an inverse relationship between two variables, y and x. To use the equation, substitute different values for x and calculate the corresponding values of y.
Step-by-step explanation:
The equation y = k/x represents an inverse relationship between two variables, y and x. Inverse relationships occur when one variable increases while the other variable decreases. For example, consider the equation y = 10/x. As x increases, y decreases. To use the equation, you can substitute different values for x and calculate the corresponding values of y.
The equation k = y/x represents a relationship between two variables, y and x, where k is the quotient of y divided by x. This equation can be used in various contexts and applications. Here are a few examples:
1. Proportional Relationships:
If the variables y and x have a proportional relationship, the equation k = y/x can be used to determine the constant of proportionality. In this case, the value of k remains the same regardless of the specific values of y and x. For example, if y represents the number of miles traveled and x represents the number of hours spent traveling, the constant k can represent the speed in miles per hour.
2. Slope of a Line:
In the context of linear equations, the equation k = y/x represents the slope of a line. The variable y represents the vertical change (or "rise") and x represents the horizontal change (or "run") between two points on the line. The value of k determines the steepness or incline of the line. A positive value of k indicates an upward slope, while a negative value indicates a downward slope.
3. Rates and Unit Conversion:
The equation k = y/x can also be used to represent rates and unit conversion. For example, if y represents the amount of money earned and x represents the number of hours worked, k can represent the earnings per hour. Similarly, if y represents the distance traveled and x represents the time taken, k can represent the speed in a specific unit (e.g., kilometers per hour or meters per second).
In summary, the equation k = y/x is a versatile tool that helps describe relationships between variables, determine constants of proportionality, calculate slopes, and represent rates and unit conversions in various contexts.