How to Find Slope From a Graph?

Answer: To find the slope from a graph, divide the change in the y-coordinate (rise) by the change in the x-coordinate (run) between two points on the line.

The slope of a line on a graph represents how steep the line is, and it’s calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line. The slope formula is:

Slope=Rise/ Run= Δy/ Δx​

Where Δy (delta y) is the change in the y-coordinate and Δx (delta x) is the change in the x-coordinate.

To calculate the slope:

1. Choose two points on the line. Let’s say these points are (x₁​,y₁​) and (x₂​,y₂).
2. Calculate the change in y (rise) by subtracting y₁ from y₂​ (y₂​−y₁​).
3. Calculate the change in x (run) by subtracting x₁ from x₂​ (i.e., x₂−x₁).
4. Divide the change in y by the change in x.

For example, if the two points on the graph are (2, 3) and (4, 7), the slope is calculated as:

Slope=7−3 ÷ 4−2= 4/2 =2

So, the slope of the line is 2. This means for every unit increase in x, y increases by 2 units.