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Chapter 1: Problem 3

Fill in the blank. The rise divided by the run is the _____ of a line.

Short Answer

Expert verified
slope

Step by step solution

01

Understanding the Concepts

First, identify the terms 'rise' and 'run' in the context of a line on a graph. 'Rise' refers to the vertical change between two points on the line, while 'run' refers to the horizontal change.
02

Contextual Definition

The ratio of the rise to the run gives a measure of the steepness or incline of a line. This ratio is a fundamental concept in coordinate geometry.
03

Identify the Term

The term that describes the ratio of the rise to the run in a line is called the 'slope'. The slope of a line represents its steepness and direction.
04

Conclusion

So, when filling in the blank, the correct term is 'slope'.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Rise and Run
The concept of 'rise' and 'run' is foundational in understanding the slope of a line. When looking at a graph, rise refers to the vertical change between two points. Imagine you are climbing a hill; the height you climb up is the rise.
On the other hand, run is the horizontal change between the same two points. Continuing the hill example, the distance you walk horizontally is the run.
The rise and run together help us describe how steep or flat a line is. These two concepts are essential for calculating the slope.
Coordinate Geometry
Coordinate geometry is an important branch of mathematics that uses a coordinate plane to describe geometric shapes and properties. Understanding how points are placed on a graph is crucial here.
In coordinate geometry, each point has two coordinates: an x-coordinate (horizontal position) and a y-coordinate (vertical position). For instance, a point might be at (3, 5), meaning it is 3 units horizontally from the origin and 5 units vertically from the origin.
When you plot two points, you can draw a line between them. The 'rise' and 'run' then help in calculating the slope of this line.
Ratio in Mathematics
A ratio is a way to compare two quantities by division. In the context of the rise and run, the slope is a ratio. The slope is calculated by dividing the rise by the run, written as \( \text{slope} = \frac{\text{rise}}{\text{run}} \).
Ratios are fundamental in various areas of mathematics since they show how one quantity relates to another. For instance, in the ratio 3:4, for every 3 units of rise, there are 4 units of run.
This concept helps in understanding the proportionality and relativity in different mathematical contexts.

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