The slope of a line passing through the points (x1,y1) and (x2,y2) is the ratio of the vertical change to the horizontal change between the points. The variable m is most commonly used to represent the slope.
rise and run is sometimes used to describe the slope of a line, especially when the line is given graphically. Rise corresponds to and run corresponds to
With this information, the definition of the slope of a line can be written in terms of rise and run.
Here, rise represents the vertical distance between points and run represents the horizontal distance. Consider the line shown. The slope of the line will be found using the following method.
To begin, mark any two points on the line. It can be helpful to mark points with integer coordinates to be as precise as possible.
Next, it is necessary to determine the rise and run between the points. This can be done in either order.
To determine the horizontal distance between points A and B, draw a line from A to the x-coordiante of B. Then, count the number of steps the segment spans. Remember, moving to the right yields a positive run, while moving to the left yields a negative run.
It can be seen that the run spans 4 units.
The rise between points can be found in the same way. Remember, moving up yields a positive rise, while moving down yields a negative rise.
The rise spans 2 units.
The slope of a line measures how y changes relative to x. There are different types of slope depending on the direction of the line.
The slope of a line can be found algebraically using the following rule.
What is the slope of the line that passes through the points (2,1) and (4,5)?