key term - Rise

Definition

The term 'rise' refers to the vertical change or increase in the y-coordinate of a point on a line. It is a key component in understanding the slope of a line, which describes the steepness and direction of the line's incline or decline.

5 Must Know Facts For Your Next Test

1. The rise of a line is the vertical change or difference in the y-coordinates between two points on the line.
2. The rise, along with the run, is used to calculate the slope of a line using the formula: slope = rise / run.
3. A positive rise indicates that the line is sloping upward, while a negative rise indicates a downward slope.
4. The magnitude of the rise, relative to the run, determines the steepness of the line, with a larger rise resulting in a steeper slope.
5. Understanding the concept of rise is crucial for interpreting the behavior and characteristics of linear functions and their graphical representations.

Review Questions

• Explain how the rise of a line is used to calculate its slope.
  • The rise of a line is the vertical change or difference in the y-coordinates between two points on the line. To calculate the slope of a line, you divide the rise by the run (the horizontal change or difference in the x-coordinates). This ratio of the vertical change to the horizontal change represents the steepness and direction of the line. A positive rise indicates an upward slope, while a negative rise indicates a downward slope.
• Describe the relationship between the rise of a line and the steepness of its slope.
  • The magnitude of the rise of a line, relative to its run, determines the steepness of the line's slope. A larger rise, with the same run, results in a steeper slope, as the line is inclined more vertically. Conversely, a smaller rise, with the same run, results in a less steep or more gradual slope. The ratio of the rise to the run is what defines the slope, so the rise is a critical factor in understanding the overall steepness and direction of a line.
• Analyze how the rise of a line affects its graphical representation on the coordinate plane.
  • The rise of a line directly impacts its graphical representation on the coordinate plane. A positive rise indicates an upward-sloping line, where the y-coordinate increases as you move from left to right. A negative rise indicates a downward-sloping line, where the y-coordinate decreases as you move from left to right. The magnitude of the rise determines the steepness of the line, with a larger rise resulting in a steeper incline or decline. Understanding the relationship between the rise and the line's graphical representation is essential for interpreting and analyzing linear functions.

Related terms

Slope:

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

Run:

The run is the horizontal change or difference in the x-coordinate between two points on a line. It is the other component, along with the rise, that is used to calculate the slope of a line.

Coordinate Plane:

The coordinate plane is a two-dimensional grid used to plot and represent points, lines, and other geometric shapes. The vertical axis represents the y-coordinate, and the rise is the change in this value.