1(y) = 1(x-1) is a mathematical expression that represents a linear equation. Let’s break it down to understand its meaning and implications.
Here’s what you need to know about 1(y) = 1(x-1):
- Definition: The equation 1(y) = 1(x-1) is a specific form of a linear equation known as a reciprocal equation. In this equation, the reciprocal of the difference between x and 1 is equal to the reciprocal of y.
- Interpretation: This equation describes a relationship between two variables, x and y, where the values of y are reciprocals of the corresponding values of (x-1). In other words, as x varies, y will change inversely.
- Example: Let’s consider a simple example to illustrate the concept. If we substitute x = 2 into the equation, we get 1(y) = 1(2-1). Simplifying this further, we have 1(y) = 1. Therefore, y must be 1 since the reciprocal of 1 is still 1.
- Graphical representation: When plotted on a graph, the equation 1(y) = 1(x-1) will result in a straight line passing through the point (1, 1) with a slope of 1. The line will extend infinitely in both directions, indicating that the relationship between x and y holds true for any value of x.
- Importance and applications: Reciprocal equations have various applications in mathematics, science, and engineering. They can be used to model relationships where one variable is inversely proportional to another. For example, in physics, the equation 1(y) = 1(x-1) might describe the relationship between the time it takes for an object to fall and the distance it travels during that time.
In conclusion, the equation 1(y) = 1(x-1) represents a reciprocal relationship between x and y. It is a linear equation with a slope of 1 and can be graphically represented as a straight line passing through the point (1, 1). Understanding reciprocal equations can be valuable in various fields and allows us to analyze inverse relationships between variables.
I hope this explanation helps! If you have any further questions, feel free to ask.