Run

Definition

In the context of graphing linear equations, understanding slope, and using the slope-intercept form, the term 'run' refers to the horizontal distance or change in the x-coordinate between two points on a line. It is a crucial component in determining the slope of a line and interpreting the equation of a line in slope-intercept form.

5 Must Know Facts For Your Next Test

1. The run of a line is the horizontal distance or change in the $x$-coordinate between two points on the line.
2. The run, along with the rise, is used to calculate the slope of a line using the formula $\text{slope} = \frac{\text{rise}}{\text{run}}$.
3. In the slope-intercept form of a linear equation, $y = mx + b$, the slope $m$ represents the ratio of the rise to the run between any two points on the line.
4. The run of a line is an essential factor in determining the direction of a line, as a positive run indicates a line sloping upward from left to right, and a negative run indicates a line sloping downward from left to right.
5. Understanding the concept of run is crucial for interpreting the graphs of linear equations and the slope-intercept form of linear equations.

Review Questions

• Explain how the run of a line is used to calculate the slope of the line.
  • The run of a line is the horizontal distance or change in the $x$-coordinate between two points on the line. The slope of a line is calculated as the ratio of the rise (the vertical distance or change in the $y$-coordinate) to the run between those two points. Specifically, the slope formula is $\text{slope} = \frac{\text{rise}}{\text{run}}$. The run is a crucial component in this formula, as it represents the horizontal change that, along with the vertical change (rise), determines the overall steepness or inclination of the line.
• Describe how the run of a line is related to the slope-intercept form of a linear equation.
  • In the slope-intercept form of a linear equation, $y = mx + b$, the slope $m$ represents the ratio of the rise to the run between any two points on the line. This means that the run, along with the rise, is a key factor in determining the slope of the line, which is represented by the coefficient $m$ in the equation. Understanding the relationship between the run, slope, and the slope-intercept form is essential for interpreting the equation of a line and visualizing its graph.
• Analyze how the direction of a line is influenced by the sign of the run.
  • The sign of the run, whether positive or negative, determines the direction of the line. A positive run indicates that the line is sloping upward from left to right, while a negative run indicates that the line is sloping downward from left to right. This is because the run represents the horizontal change between two points on the line, and the direction of this change, along with the direction of the vertical change (rise), determines the overall orientation of the line. Analyzing the sign of the run is crucial for understanding the direction and behavior of a linear equation's graph.

Related terms

Rise:

The vertical distance or change in the y-coordinate between two points on a line, which is also a key factor in determining the slope of a line.

Slope:

The measure of the steepness or inclination of a line, calculated as the ratio of the rise to the run between two points on the line.

Slope-Intercept Form:

The equation of a line written in the form $y = mx + b$, where $m$ represents the slope of the line and $b$ represents the $y$-intercept.