Equation of a Straight Line
📐 What is the Equation of a Straight Line?
The equation of a straight line is an algebraic expression that describes every point $(x, y)$ that lies on that line. It establishes a relationship between the $x$-coordinate and $y$-coordinate of all points on the line.
Key Idea: A straight line is completely determined by two things — its slope (steepness) and its position (where it sits on the coordinate plane).
📏 The Slope (Gradient)
The slope (denoted by $m$) measures how steep a line is. Given two points $(x_1, y_1)$ and $(x_2, y_2)$ on a line:
$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{\text{Rise}}{\text{Run}} $$
- $m > 0$ → Line goes upward (left to right)
- $m < 0$ → Line goes downward (left to right)
- $m = 0$ → Line is horizontal
- $m$ is undefined → Line is vertical
Interactive visualization — available in the full lesson