key term - Rise

Definition

In the context of slope of a line, the term 'rise' refers to the vertical change or the change in the y-coordinate between two points on a line. It represents the vertical distance traveled as you move from one point to another on the line.

5 Must Know Facts For Your Next Test

1. The rise of a line is the vertical distance between two points on the line, and it is typically represented by the variable 'y' or 'Δy'.
2. The rise of a line is the first part of the slope formula, which is expressed as the change in y-coordinate divided by the change in x-coordinate.
3. A positive rise indicates that the line is sloping upward, while a negative rise indicates that the line is sloping downward.
4. The magnitude of the rise, along with the run, determines the steepness or slope of the line, with a larger rise resulting in a steeper slope.
5. Understanding the concept of rise is crucial in interpreting the behavior and characteristics of a linear function, as it directly impacts the slope and the overall shape of the line.

Review Questions

• Explain how the rise of a line is used to calculate the slope.
  • The rise of a line is the vertical change or the change in the y-coordinate between two points on the line. To calculate the slope of a line, you use the rise-over-run formula, which involves dividing the rise (change in y-coordinate) by the run (change in x-coordinate) between any two points on the line. The rise is the first part of this formula and is essential for determining the steepness or incline of the line.
• Describe the relationship between the rise of a line and the direction of the line.
  • The rise of a line can indicate the direction of the line. A positive rise means the line is sloping upward, while a negative rise means the line is sloping downward. The magnitude of the rise, along with the run, determines the overall steepness or slope of the line. A larger rise results in a steeper slope, while a smaller rise results in a gentler slope. Understanding the relationship between the rise and the direction of the line is crucial for interpreting the behavior and characteristics of a linear function.
• Analyze how the rise of a line is used to classify the type of linear function.
  • $$The rise of a line is a key factor in determining the type of linear function. A line with a positive rise represents a function that is increasing, while a line with a negative rise represents a function that is decreasing. The magnitude of the rise also affects the steepness of the line, which can be used to classify the function as having a steep, moderate, or gentle slope. Additionally, the rise can be used to identify the y-intercept of the line, which is the point where the line crosses the y-axis. Understanding the rise of a line is essential for analyzing the properties and behavior of linear functions.$$

Related terms

Slope:

The slope of a line is the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. It represents the steepness or incline of the line.

Run:

The run is the horizontal change or the change in the x-coordinate between two points on a line. It represents the horizontal distance traveled as you move from one point to another on the line.

Rise-over-Run: The rise-over-run formula, also known as the slope formula, is used to calculate the slope of a line by dividing the rise (vertical change) by the run (horizontal change) between two points.