Determining the Slope of a Line From Its Graph

The slope of a line measures the change between points on the line. When presented graphically, it is common to use the following definition of slope. m=rise/run Here, rise represents the vertical distance between points. Whereas, run represents the horizontal distance between points. Consider the following line.

The slope of this line can be found using the following four steps.

1

Mark Two Points on the Line

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To begin, mark any two points on the line. It is helpful to mark points with integer coordinates. This helps with accuracy.

From here, it is necessary to determine the rise and run between the points. Note that this can be done in either order.

2

Determine the Run

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Draw a line from A to the x-coordinate of point B to determine the horizontal distance between the points. Then, count the number of steps the line segment spans. Recall that moving to the right results in a positive run, while moving to the left results in a negative run.

In this graph, the run spans 4 units and it is positive.

3

Determine the Rise

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The rise between points can be found in the same way. Remember, moving up results in a positive rise and moving down results in a negative rise.

The rise spans 2 units and it is also positive.