Run

Definition

In the context of understanding the slope of a line, the term 'run' refers to the horizontal distance or change in the x-coordinate between two points on a line. It is one of the key components used to calculate the slope of a line, along with the 'rise' or change in the y-coordinate between the same two points.

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 is one of the two components, along with the rise, used to calculate the slope of a line.
3. The slope of a line is the ratio of the rise to the run, and it represents the steepness or incline of the line.
4. The run is a crucial factor in determining the direction and steepness of a line on a coordinate plane.
5. Understanding the concept of run is essential for interpreting and graphing linear functions, as well as for solving problems involving the slope of a line.

Review Questions

• Explain the role of the run in calculating the slope of a line.
  • The run, which represents the horizontal distance or change in the x-coordinate between two points on a line, is a key component in calculating the slope of that line. The slope is determined by the ratio of the rise (change in y-coordinate) to the run (change in x-coordinate) between those two points. The run, along with the rise, provides the necessary information to determine the steepness or incline of the line, which is a crucial characteristic in understanding and working with linear functions.
• Describe how the run of a line is used to determine the direction of the line on a coordinate plane.
  • The direction of a line on a coordinate plane is determined by the sign of the slope, which is calculated using the run and rise between two points. If the run is positive (the x-coordinate is increasing from the first point to the second), and the rise is also positive, the line has a positive slope and is sloping upward from left to right. If the run is positive, but the rise is negative, the line has a negative slope and is sloping downward from left to right. The run, therefore, plays a crucial role in identifying the direction and orientation of a line on the coordinate plane.
• Analyze how the value of the run can be used to infer information about the steepness or incline of a line.
  • The value of the run, in combination with the rise, directly determines the slope of a line, which represents its steepness or incline. If the run is small compared to the rise, the slope will be large, indicating a steep or sharply inclined line. Conversely, if the run is large compared to the rise, the slope will be small, indicating a line that is relatively flat or gently inclined. Therefore, the magnitude of the run can provide valuable insights into the overall steepness of the line, which is an important characteristic in understanding and working with linear functions and their real-world applications.

Related terms

Rise: The change in the y-coordinate between two points on a line, used along with the 'run' to calculate the slope.

Slope: The measure of the steepness or incline of a line, calculated as the ratio of the 'rise' to the 'run' between two points.

Coordinate Plane: A two-dimensional plane with x and y axes, used to plot and analyze the relationship between variables.