Equation of a Line

When discussing the equation of a line in mathematics, we are referring to the formula that describes a straight line on a graph. The equation takes the general form of y = mx + b, where y is the dependent variable, x is the independent variable, m is the slope of the line, and b is the y-intercept.

Slope-Intercept Form

The most commonly used form of the equation of a line is the slope-intercept form, y = mx + b. In this form, the slope (m) represents the rate at which the line rises or falls, while the y-intercept (b) is the point at which the line intersects the y-axis.

Point-Slope Form

Another form of the equation of a line is the point-slope form, which is written as y - y₁ = m(x - x₁). In this form, (x₁, y₁) represents a specific point on the line, and m is the slope of the line.

Standard Form

The standard form of a line's equation is Ax + By = C, where A, B, and C are constants. This form is useful for finding the equation of a line when given two points on the line. The equation can be rearranged into the slope-intercept form for easier interpretation.

In conclusion, the equation of a line is a fundamental concept in mathematics that allows us to describe and analyze linear relationships in various contexts.