In a linear equation, what is the highest exponent of the variable?

In a linear equation, the defining characteristic is that it represents a straight line when graphed. This is due to the variables in the equation being raised to the first power only. Therefore, the highest exponent of the variable in a linear equation is indeed 1.

For example, consider the equation of a line in the slope-intercept form, which is typically written as (y = mx + b), where (m) represents the slope and (b) the y-intercept. In this equation, the variable (x) is raised to the first power, confirming that the degree of the polynomial is 1. This straightforward relationship between the input and output variables is what allows for the direct and proportional representation of changes on a Cartesian plane.

Higher exponents, such as 2 or 3, would indicate quadratic or cubic equations, respectively, which do not graph as straight lines but rather as curves. An exponent of 0 implies a constant, as it depicts the horizontal line where the y-value remains the same regardless of the x-value. Therefore, the correct representation of a linear equation confirms that the highest exponent of the variable is 1.