Slope

Definition

Slope measures the steepness and direction of a line, typically defined as the ratio of the vertical change to the horizontal change between two points on the line. It is commonly represented by the letter $m$.

5 Must Know Facts For Your Next Test

1. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$ where $(x_1, y_1)$ and $(x_2, y_2)$ are two distinct points on a line.
2. A positive slope indicates that the line rises as it moves from left to right.
3. A negative slope indicates that the line falls as it moves from left to right.
4. A slope of zero indicates a horizontal line, while an undefined slope (division by zero) indicates a vertical line.
5. Slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Review Questions

• What does a positive slope indicate about a linear function?
• How do you calculate the slope given two points on a line?
• What is the significance of an undefined slope?

Related terms

Y-Intercept: The point where a line crosses the y-axis, represented by $b$ in the equation $y = mx + b$.

Linear Equation: An equation that makes a straight line when graphed. It has no variables with exponents greater than one.

Rate of Change: A measure of how much one quantity changes in relation to another quantity; in linear functions, this is synonymous with slope.