Explanation:
Slope is rise (vertical distance) over run (horizontal distance), or rise divided by run. The rise and the run are differences in coordinates that you find by doing two subtractions.
Find two points on the line and identify and x- and y-coordinates of the two points. To find the rise, subtract one y-coordinate from the other. To find the run, subtract one x-coordinate from the other in the same order you did the subtraction of the y-coordinates. Divide the rise (difference in y) by the run (difference in x). That is the slope.
Example: You see the graph of a line, and you read off points (6, 5) and (2, 3). The y-coordinates of the two points are 5 and 3. The x-coordinates, in the same order, are 6 and 2. The rise is 5 - 3 = 2. The run is 6 - 2 = 4. Divide the rise by the run: 2/4 and reduce to 1/2. The slope of the line is 1/2.