This section provides step-by-step examples on how to apply linear equation concepts. You'll learn how to find slopes, write equations in different forms, determine the relationships between lines, and solve applications.

Linear equations can be written in Slope-Intercept form ($y = mx + b$), Point-Slope form ($y - y_1 = m(x - x_1)$), or Standard form ($Ax + By = C$). You must know how to convert between them.

Calculating the distance between two points and finding the exact middle point on a coordinate plane.

The slope ($m$) of a line measures its steepness and direction. It is defined as the "rise" over the "run" between any two points $(x_1, y_1)$ and $(x_2, y_2)$ on the line: $m = \frac{y_2 - y_1}{x_2 - x_1}$.

Parallel lines never intersect and have the exact same slope ($m_1 = m_2$). Perpendicular lines intersect at a 90-degree angle and have slopes that are negative reciprocals of each other ($m_1 \cdot m_2 = -1$).