Look for the representation of slope within a line's equation. The equation may be in standard form or in slope intercept form. For example, you could have y = 2x + 6 (slope intercept) or 2x -y + 6 = 0 (standard). Both of these equations belong to the same line. In either equation, the "x" denotes slope.
View the degree of the slope as a fraction that indicates rise over run. In this example, the slope is 2. If you write 2 as a fraction, you would write 2/1. This means that for each two units that the line rises, it runs one unit. Rise is charted on the vertical (y) axis, and run is charted on the horizontal (x) axis.
Look for the sign of the "x" term to determine the direction of the slope. If the "x" term has no sign or has a plus sign preceding it, then the line has a positive slope and will be heading in an upward direction from left to right. If the "x" term has a minus sign preceding it, then the line has a negative slope and will be heading downward from left to right. If you don't have the linear equation, you can simply look at the line to see if its slope is negative or positive.
Use sets of points on a line to determine the slope if you don't have the equation of the line. A set of points consists of an "x" and a "y" coordinate, as in (3, 4). Look at two points on the line. Subtract the second "y" coordinate from the first "y" coordinate. Then subtract the second "x" coordinate from the first "x" coordinate. The write a fraction with the "y" answer as the numerator and the "x" answer as the denominator. Consider the following example points: (3, 5) and (1, 4). Subtract 4 from 5 to get 1. Subtract 1 from 3 to get 2. Write the fraction 1/2 as the slope. This means that the slope is positive, and the line rises one unit when it runs two.