The independent variable in the equation y=5x-6 is x.
In mathematics, an independent variable is a variable that can be freely chosen or manipulated. It is the variable that is not dependent on any other variable in the equation. In this equation, y is the dependent variable because its value depends on the value of x. The value of y changes based on the value of x, but x does not depend on y.
To understand this concept further, let's break down the equation y=5x-6. The equation represents a linear relationship between two variables, y and x. The coefficient 5 in front of x indicates that for every unit increase in x, y will increase by 5 units. The constant term -6 represents a vertical shift downwards by 6 units.
By manipulating or choosing different values for x, we can determine corresponding values for y. For example, if we set x=0, then y=-6. If we set x=1, then y=5(1)-6=-1. If we set x=2, then y=5(2)-6=4. And so on.
It is important to note that the choice of which variable is independent or dependent depends on the context of the problem or equation being analyzed. In this particular equation, x is chosen as the independent variable because it can be freely chosen or manipulated to determine the corresponding values of y.