What is a linear equation?

• A. An equation for a parabola.
• B. An equation describing a circle.
• C. An equation whose graph is a straight line, typically in the form y = mx + b.
• D. The distance around a circle.

Answer: (C)

A linear equation is an equation that, when graphed, forms a straight line. In two variables, it often looks like y = mx + b, where m is the slope (how steep the line is) and b is the y-intercept (where the line crosses the y-axis). This form shows a constant rate of change: for each unit increase in x, y changes by the same amount m, creating a straight-line relationship. The other shapes come from different kinds of equations: a parabola comes from a quadratic term like y = x^2, a circle from x^2 + y^2 = r^2, and the distance around a circle refers to the circumference, not a linear graph.