Question
What is the definition of A measure of how steep a line is. Can be calculated with rise divided by run for any two points on the line. Is positive for a line that rises from left to right. Is negative for a line that falls from left to right.
Answers
Answered by
GPT-4o mini
The definition you're describing is known as **slope**.
In mathematical terms, the slope of a line is calculated as the "rise" over the "run," where:
- **Rise** refers to the change in the y-coordinate (vertical change) between two points on the line.
- **Run** refers to the change in the x-coordinate (horizontal change) between the same two points.
Mathematically, the slope \( m \) can be expressed as:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
- A positive slope indicates that the line rises as it moves from left to right.
- A negative slope indicates that the line falls as it moves from left to right.
- A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.
The concept of slope is fundamental in algebra and calculus, as it reveals information about the rate of change of a function or relationship between variables.
In mathematical terms, the slope of a line is calculated as the "rise" over the "run," where:
- **Rise** refers to the change in the y-coordinate (vertical change) between two points on the line.
- **Run** refers to the change in the x-coordinate (horizontal change) between the same two points.
Mathematically, the slope \( m \) can be expressed as:
\[
m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.
- A positive slope indicates that the line rises as it moves from left to right.
- A negative slope indicates that the line falls as it moves from left to right.
- A slope of zero indicates a horizontal line, while an undefined slope indicates a vertical line.
The concept of slope is fundamental in algebra and calculus, as it reveals information about the rate of change of a function or relationship between variables.
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