To find or calculate the slope of a line, follow these steps:
What is Slope?
- Slope measures how steep a line is, often described as "rise over run," which means how much the line goes up or down (vertical change) divided by how far it goes left or right (horizontal change)
How to Calculate Slope
- Select Two Points on the Line
Choose any two points on the line. Label them as (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2)
- Calculate the Change in Y and X
- Change in y (rise) = y2−y1y_2-y_1y2−y1
- Change in x (run) = x2−x1x_2-x_1x2−x1
- Apply the Slope Formula
m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
where mmm is the slope
- Interpret the Result
- If the slope is positive, the line rises from left to right.
- If the slope is negative, the line falls from left to right.
- If the slope is zero, the line is horizontal.
- If the slope is undefined (division by zero), the line is vertical
Example
If you pick points (1,2)(1,2)(1,2) and (5,−4)(5,-4)(5,−4):
- Change in y = −4−2=−6-4-2=-6−4−2=−6
- Change in x = 5−1=45-1=45−1=4
- Slope m=−64=−32m=\frac{-6}{4}=-\frac{3}{2}m=4−6=−23
Finding Slope from a Graph
- Pick two points on the line with clear coordinates.
- Count how many units you go up or down (rise) and how many units you go right or left (run).
- Use the rise/run formula, considering direction (up/right positive, down/left negative)
This method works for any line and is a fundamental concept in algebra and coordinate geometry
