Bot GPT 4-o mini It looks like you're looking for a complete explanation of the slope of a line, including the formula and related terms. I'll fill in the blanks accordingly:
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Slope is the answer of a line.
Answer: True, the slope represents the steepness of the line. -
Slope equals the rise divided by the run for any two points on the line.
Answer: slope. -
The rise is the vertical distance between the points, and the run is the horizontal distance.
Answer: horizontal.
We can count these distances, or we could use the distance formula.
When given 2 points on a line as the ordered pairs (x1, y1) and (x2, y2), the slope (abbreviated m) is equal to:
\[ m = \frac{y2 - y1}{x2 - x1} \]
Where:
- y2 and y1 are the y-coordinates of the two points,
- x2 and x1 are the x-coordinates of the two points.
Summary of Terms:
- M: The slope of the line.
- Rise: The change in the y-coordinates (vertical change, \( y2 - y1 \)).
- Run: The change in the x-coordinates (horizontal change, \( x2 - x1 \)).
- Steepness: A qualitative description of the slope, where a larger absolute value of the slope indicates a steeper line.
Use this information to calculate and understand the slope of a line based on two points!
1 answer