To find the slope of a line, you need two points on the line, each with coordinates (x1,y1)(x_1,y_1)(x1,y1) and (x2,y2)(x_2,y_2)(x2,y2). The slope mmm is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between these points, using the formula:
m=y2−y1x2−x1m=\frac{y_2-y_1}{x_2-x_1}m=x2−x1y2−y1
Here's how to find it step-by-step:
- Identify two points on the line and note their coordinates.
- Calculate the difference in the y-values: Δy=y2−y1\Delta y=y_2-y_1Δy=y2−y1 (rise).
- Calculate the difference in the x-values: Δx=x2−x1\Delta x=x_2-x_1Δx=x2−x1 (run).
- Divide the rise by the run to get the slope: m=ΔyΔxm=\frac{\Delta y}{\Delta x}m=ΔxΔy.
For example, if the points are (2, 5) and (9, 19):
- Δy=19−5=14\Delta y=19-5=14Δy=19−5=14
- Δx=9−2=7\Delta x=9-2=7Δx=9−2=7
- Slope m=147=2m=\frac{14}{7}=2m=714=2
This means the line rises 2 units vertically for every 1 unit it moves horizontally
. Additional notes:
- If the line goes up as you move from left to right, the slope is positive.
- If it goes down, the slope is negative.
- A horizontal line has a slope of 0.
- A vertical line has an undefined slope
