\[ y = mx + b \]
where:
- \( y \) is the dependent variable (often called the output or the value being solved for),
- \( x \) is the independent variable (often called the input or the value being manipulated),
- \( m \) is the slope of the line, which represents the rate of change of \( y \) with respect to \( x \),
- \( b \) is the y-intercept, which is the value of \( y \) when \( x = 0 \).
Linear equations can also be represented in standard form:
\[ Ax + By = C \]
where \( A \), \( B \), and \( C \) are constants, and \( A \) and \( B \) are not both zero.
Linear equations can be solved algebraically by isolating the dependent variable \( y \) or \( x \), or by graphing the equation and finding the intersection point(s) with the x-axis or y-axis. These equations are fundamental in various areas of mathematics, science, engineering, economics, and more, for modeling relationships that exhibit a constant rate of change.