What does a linear equation describe when graphed?

A linear equation, when graphed on a coordinate plane, describes a straight line. This occurs because a linear equation can be expressed in the standard form (y = mx + b), where (m) represents the slope of the line and (b) is the y-intercept. The slope indicates the rate of change of (y) in relation to (x), resulting in a constant rate of increase or decrease, which is characteristic of linear relationships.

In contrast, other options describe different types of graphical representations. A curve with variable slope suggests a nonlinear relationship, which is not applicable to linear equations. The layout of a geometric figure typically refers to the arrangement of various shapes and does not correlate specifically with linear equations. Lastly, a set of discrete points would involve distinct values of (x) and (y) that do not form a continuous line, which also does not fit the description of a linear equation. Therefore, the correct answer accurately depicts the nature of linear equations in graphical terms.