How to Find Slope From a Graph? (original) (raw)

Last Updated : 23 Jul, 2025

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= Δ__y/_ Δ__x_​

Where Δ__y_ (delta y) is the change in the y-coordinate and Δ__x_ (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 (_x _1_​,_y _1_​) and (_x _2_​,_y 2).
  2. Calculate the change in y (rise) by subtracting y1 from _y _2_​ (_y 2_​−__y _1_​).
  3. Calculate the change in x (run) by subtracting _x 1 from _x _2_​ (i.e., _x _2_−__x_1).
  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.

Similar Questions

What is the Slope?

The slope of a line on a graph represents the rate of change or the steepness of the line. It is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Can the Slope Be Negative?

Yes, the slope can be negative if the line is decreasing (moving downwards as it moves from left to right on the graph). A negative slope indicates that as the x-values increase, the y-values decrease.

What Does a Slope of Zero Mean?

A slope of zero means the line is horizontal. This indicates no vertical change (rise) regardless of the horizontal change (run), so the y-value remains constant.

How Do You Interpret a Positive Slope?

A positive slope indicates that the line is increasing, meaning as the x-values increase, the y-values also increase. The line moves upwards from left to right.

What if the Slope is Undefined?

The slope is undefined when the line is vertical. This happens because the run (horizontal change) is zero, and dividing by zero is undefined.