(628)-272-0788 info@etutorworld.com
Select Page

# Slope from a Graph

To find the slope of a line from a graph, you need to identify two points on the line. The slope of the line is equal to the change in y divided by the change in x between the two points.

• Slope from a Graph
• Solved Examples
• FAQs

Personalized Online Tutoring

## Slope from a Graph

To find the slope of a line from a graph, you need to identify two points on the line. The slope of the line is equal to the change in y divided by the change in x between the two points.

Let’s say you have a graph of a line and you want to find its slope. Here’s how you can do it:

Identify two points on the line. You can choose any two points as long as they are on the line. Let’s call these points (x1, y1) and (x2, y2).

Calculate the change in y between the two points. This is equal to y2 – y1.

Calculate the change in x between the two points. This is equal to x2 – x1.

Divide the change in y by the change in x to get the slope of the line. This is equal to (y2 – y1) / (x2 – x1).

For example, let’s say you have the line passing through the points (2, 3) and (5, 9). To find the slope of the line, we can use the formula:

slope = (y2 – y1) / (x2 – x1)

where (x1, y1) = (2, 3) and (x2, y2) = (5, 9). Substituting these values into the formula, we get:

slope = (9 – 3) / (5 – 2)

= 6 / 3

= 2

So, the slope of the line passing through the points (2, 3) and (5, 9) is 2.

There have been times when we booked them last minute, but the teachers have been extremely well-prepared and the help desk at etutorworld is very prompt.

Our kid is doing much better with a higher score.

- Meg, Parent (via TrustSpot.io)

Solved Examples

Example 1: Find the slope of the line passing through the points (-2, 4) and (3, 8).

Solution: Using the formula for slope, we have:

slope = (y2 – y1) / (x2 – x1)

where (x1, y1) = (-2, 4) and (x2, y2) = (3, 8).

Substituting these values into the formula, we get:

slope = (8 – 4) / (3 – (-2))

= 4 / 5

Therefore, the slope of the line passing through the points (-2, 4) and (3, 8) is 4/5.

Example 2: Find the slope of the line passing through the points (0, -3) and (4, 5).

Solution: Using the formula for slope, we have:

slope = (y2 – y1) / (x2 – x1)

where (x1, y1) = (0, -3) and (x2, y2) = (4, 5).

Substituting these values into the formula, we get:

slope = (5 – (-3)) / (4 – 0)

= 8 / 4

= 2

Therefore, the slope of the line passing through the points (0, -3) and (4, 5) is 2.

Example 3: Find the slope of the line passing through the points (2, 1) and (2, 5).

Solution: Using the formula for slope, we have:

slope = (y2 – y1) / (x2 – x1)

where (x1, y1) = (2, 1) and (x2, y2) = (2, 5).

Substituting these values into the formula, we get:

slope = (5 – 1) / (2 – 2)

However, the denominator is 0, which means that the slope is undefined. This is because the line passing through the points (2, 1) and (2, 5) is a vertical line, and vertical lines have undefined slope.

Therefore, the slope of the line passing through the points (2, 1) and (2, 5) is undefined.

## FAQS

##### What is the slope of a horizontal line?

The slope of a horizontal line is 0, because the line has no vertical change (change in y) between any two points.

##### What is the slope of a vertical line?

The slope of a vertical line is undefined, because the line has no horizontal change (change in x) between any two points.

##### Can the slope of a line be negative?

Yes, the slope of a line can be negative if the line is slanting downwards from left to right.

##### How do I find the slope of a line if I only have one point?

You cannot find the slope of a line with only one point. You need at least two points to find the slope of a line using the formula: slope = (y2 – y1) / (x2 – x1).

##### Can I use any two points on a line to find the slope?

Yes, you can use any two points on a line to find the slope, as long as the points are not vertically aligned.

Gloria Mathew writes on math topics for K-12. A trained writer and communicator, she makes math accessible and understandable to students at all levels. Her ability to explain complex math concepts with easy to understand examples helps students master math. LinkedIn

## IN THE NEWS

Our mission is to provide high quality online tutoring services, using state of the art Internet technology, to school students worldwide.