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.

Table of Contents:

• Slope from a Graph
• Solved Examples
• FAQs

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.

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

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