Final answer:
In mathematics, a variable represents a quantity that can change; in linear equations, x and y are variables with x typically representing the independent variable and y the dependent variable.
Step-by-step explanation:
In mathematics, a variable is a symbol that represents a quantity in a mathematical expression, equation, or function that can change. For instance, in the equation of a line, which is typically written in the form y = mx + b, the variables are represented by x and y. Here, x is the independent variable and is usually plotted on the horizontal axis, while y is the dependent variable, plotted on the vertical axis. The values of x and y can change depending on the particular points along the line. The constants m and b in the equation determine the slope and the y-intercept of the line respectively, which dictate the shape and position of the line on the graph.
Let's illustrate this with a numerical example. If we have the equation y = 2x + 3, and we want to find the value of y when x is 5, we substitute 5 for x resulting in y = 2(5) + 3, which simplifies to y = 10 + 3, and finally y = 13. In this case, 5 and 13 are the specific values of the variables x and y for this instance, but x and y can take on many different values which is why they are called variables.