How To Find Slope From Graph? Examples

How to Find Slope From a Graph?

The process of finding the slope from graph uses the slope formula rise/run. When the graph of a line is given and we are asked to find its equation, the first thing that we have to do is to find it slope. We can choose any two points (x₁, y₁) and (x₂, y₂) on the line and use the formula (y₂ - y₁) / (x₂ - x₁) for calculating the slope from a graph.

Let us see more ways of calculating slope from a graph along with more examples. Let us also learn how to find the slope of horizontal and vertical lines.

1.	Finding Slope From a Graph
2.	Calculating Slope From Graph Using Slope Formula
3.	Finding Slope of a Horizontal Line From a Graph
4.	Finding Slope of a Vertical Line From a Graph
5.	FAQs on How to Find Slope From a Graph

Finding Slope From a Graph

The slope of a line is the ratio of rise to run. Hence, here are the steps to find slope from a graph.

• Select any two random points on the graph of the line (preferably with integer coordinates).
• Label them as A and B (in any order).
• Calculate the "rise" from A to B. While going vertically from A to B, if we have to go "up", then the rise is positive; "down", then the rise is negative.
• Calculate the "run" from A to B. While going horizontally from A to B, if we have to go "right", then the run is positive; "left", then the run is negative.
• Now, use the formula: slope = rise/run.

Here is an example of the graph of a line.

Here, we have taken A = (1, 1) and B = (0, 3). Note that we have taken the points with integer coordinates here. Make a right-angled triangle starting from A and ending at B which makes the process of finding rise and run easier. Here, we have to move vertically "up" to reach B from A and hence rise = +2; and we have to move horizontally "left" to reach from A to B and hence run = -1. So slope = rise/run = 2/-1= -2.

We do not need to choose these points only to calculate the slope and also we do not need to choose them in the above order. Here you can see the graph of the same line where the same points are chosen in a different order and different points are chosen. Observe that the slope of the line (final answer) will be ultimately the same.

Calculating Slope From Graph Using Slope Formula

The slope formula is used to find the slope of a line that joins two points (x₁, y₁) and (x₂, y₂). Using this formula, the slope of the line is, m = (y₂ - y₁) / (x₂ - x₁). We can use the same formula to find the slope of a line from its graph also. For this:

• Pick any two points on the line from its graph.
• Represent them as (x₁, y₁) and (x₂, y₂) in any order.
• Apply the formula m = (y₂ - y₁) / (x₂ - x₁) to find the slope.

Example: Consider the above graphs. Let us choose two points (-1, 5) and (1, 1) on it. Now, let

• (x₁, y₁) = (-1, 5)
• (x₂, y₂) = (1, 1)

Slope, m = (y₂ - y₁) / (x₂ - x₁) = (1 - 5) / (1 - (-1)) = -4/2 = -2

We had got the same slope (-2) when we calculated the slope using rise/run also.

Finding Slope of a Horizontal Line From a Graph

A horizontal line is a line that is parallel to the x-axis. So all points on a horizontal line have the same y-coordinates. Thus, for any two points on a horizontal line, the rise = 0. Hence, the slope = rise/run = 0/run = 0. Hence, the slope of a horizontal line is always 0. Here is an example.

Here, the slope of the horizontal line y = 3 is calculated using both methods rise/run and (y₂ - y₁) / (x₂ - x₁). You can notice that the slope in both cases is 0.

Finding Slope of a Vertical Line From a Graph

A vertical line is always parallel to the y-axis. Thus, all points on a vertical line have the same x-coordinates. Thus, for any two points on it, the run = 0. Hence, the slope = rise/run = rise/0 = undefined. Hence, the slope of a vertical line is always undefined. Here is an example.

Here, the slope of the vertical line x = 3 is calculated using both formulas rise/run and (y₂ - y₁) / (x₂ - x₁). You can notice that the slope in both cases is undefined.

Important Notes on Finding Slope From a Graph

• The slope from graph can be calculated by picking any two points on it and applying the formula rise/run.
• It can be also found by picking two points and applying the formula (y₂ - y₁) / (x₂ - x₁).
• The slope of a horizontal line is 0 always.
• The slope of a vertical line is undefined always.

☛ Related Topics:

• Point Slope Form Calculator
• Finding Slope From Two Points Calculator
• Slope Intercept Form Calculator
• Equation of Line Calculator