A slope is the angle of a line from the horizontal position. Imagine a ramp leading to a doorway; this is a slope. It is at an angle, compared to the flat, even ground leading up to it. Parallel lines are lines which are at the same angle. Double yellow lines along a road are parallel lines because they run in exactly the same direction. Therefore, a parallel slope is defined by lines which run parallel; or at the same angle. If you carried on drawing both the lines indefinitely, they would never cross over.
Compare parallel slopes with perpendicular lines, to make sure you have identified the slope correctly. At the most basic level, two lines which are at a right angle to one another are known as perpendicular lines. The lines intersect. In mathematical terms, the slopes of perpendicular lines have negative reciprocals. This means on a graph one coordinate will be negative for one line, while the respective coordinate for the second line will be positive. A corner is an example of perpendicular lines.
To measure the angle of a parallel slope you will need a protractor, ruler, pencil and graph paper. The simplest way to find the angle is to draw a horizontal line directly below the slope, so that the endpoint of the slope line intersects with it. Now, position the vertex of the protractor at this point. Make sure 0 degrees and horizontal bottom edge of the protractor is in line with the line you just drew. Now, follow the line of the slope toward the edge of the protractor. Read this number; this is the angle of the slope.
It is possible to solve mathematical problems associated with parallel slopes with algebra, although the equations for a beginner are complex. For example, in an exam the question might be, "Given the line 2x -- 3y = 9 and the point (4, --1), find lines through the point that are (a) parallel to the given line and (b) perpendicular to it." In this instance, to answer the question, you need to compare two points on a graph and perform a calculation to find the angle of the slope line, and coordinates for the perpendicular line.