Subtract the y-coordinate of the first point from the y-coordinate of the second point. Two-dimensional graph coordinates come in ordered pairs enclosed in parentheses, with the x-coordinate listed first and the y-coordinate listed second. So for example if the points (5,8) and (9,3) were on a straight line, 3 - 8 = -5 would be the difference of the y-coordinates.
Subtract the x-coordinate of the first point from the x-coordinate of the second point. To continue the example, you'd have 9 - 5 = 4.
Write the two differences you calculated as a ratio with the difference of the y-coordinates -- your result from Step 1 -- on top and the difference of the x-coordinates -- your result from Step 2 -- on the bottom. The complete the example, your result is (-5)/4. Because the number is negative, you know the line goes down as you read it from left to right. And because the absolute value of your numerator is greater than the absolute value of your denominator, you know the line sinks at a steeper-than-45-degree angle.
Examine the equation you've been given for the line, and perform any algebraic operations necessary to render it in one of two accepted standard forms: Slope-intercept form is y = mx + b, and the point-slope form is y - ysub1 = m(x - xsub1). In each equation, m, b, ysub1 and xsub1 are replaced by numbers. Not all of the elements are present; if any element is missing, for example if ysub1 is absent, it is understood to be zero.
Write the number occupying the place where "m" sits in the standard equation forms. This number represents the slope of the line. So if your slope-intercept equation for a line is y = (1/2)x + 4, the line's slope is 1/2. If your point-slope equation is y - 5 = 3(x - 5), the line's slope is 3.
Interpret the line's slope, based on the number you just extrapolated from the equation. Because the slope of 1/2 you got from the slope-intercept equation is positive, the line rises from left to right. For every one unit the line moves up, it moves two units across.
Because the slope of 3 you got from the point-slope equation is positive, that line also rises as you read it from left to right. When a line's slope is written as an integer, it's understood to be a fraction with a denominator of one; so this slope is actually 3/1. This tells you that for every three units the line moves up, it moves one unit across.