There are two components to the slope of a line: its direction and its magnitude. Find the slope of a line by observing whether, from left to right, the line rises or falls and whether the line is vertical or horizontal. Then, take the coordinates of any two points on the line and divide the difference in the points' y-axis values by the difference in their x-axis values.
The equation for calculating the magnitude of the slope, where m is the slope of a line with x and y coordinates and ? is change, is m=?y/?x. To apply this formula, pick any two points on the line, and determine their x and y coordinates. The x value indicates the point's position on the horizontal axis; y is its position on the vertical axis. Subtract the y-coordinate of the first point from the y coordinate of the second point. Then, subtract the x-coordinate of the first point from the x-coordinate of the second point. Divide the difference in y-coordinates by the difference in x-coordinates. The resulting quotient is the magnitude of the slope, which indicates the steepness of the slope; the greater the slope, the steeper the line. The slope of a line may be positive, negative, zero or undefined. If a line rises from left to right, the direction of the slope is positive. If a line falls from left to right, the direction of the slope is negative. A horizontal line has a slope of zero. The slope of a vertical line is undefined, because on a vertical line, the change in x-coordinates between any two points is zero, making the denominator of ?x in the slope equation zero. Fractions with a denominator of zero are undefined.