To find the slope of a line, you can use the formula:
m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
Here, mmm is the slope of the line, (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2) are the coordinates of any two distinct points on the line.
Steps to find the slope:
- Identify two points on the line. Each point has coordinates (x,y)(x,y)(x,y).
- Calculate the difference in the y-coordinates: Δy=y2−y1\Delta y=y_2-y_1Δy=y2−y1 (this is called the "rise").
- Calculate the difference in the x-coordinates: Δx=x2−x1\Delta x=x_2-x_1Δx=x2−x1 (this is called the "run").
- Divide the change in y by the change in x: m=ΔyΔxm=\frac{\Delta y}{\Delta x}m=ΔxΔy.
This gives you the steepness or inclination of the line. The slope tells you how much yyy changes for a unit change in xxx.
- A positive slope means the line rises from left to right.
- A negative slope means the line falls from left to right.
- A zero slope means the line is horizontal.
- An undefined slope means the line is vertical.
The slope formula works for any two points on the line and the value will be the same. This is often summarized as "slope = rise over run" — the vertical change divided by the horizontal change between two points on the line.
If you'd like, I can provide an example calculation.
