Use a triangle drawn beneath a line to define the slope of the line. Drop a line down for a short distance from any point along the graphed line. From this point, draw another short horizontal line back to the graphed line. You should now have a right triangle where the hypotenuse is formed by the graphed line. The slope of the line is the height of this triangle divided by the base of the triangle. As the line becomes more and more vertical, the slope increases. As the line becomes more and more horizontal, the slope becomes smaller and smaller. The slope of a horizontal line is zero.
Put the formula for a line in the slope-intercept form to see the slope without drawing the defining triangle. The slope-intercept of a linear equation is y = mx + b, where "m" and "b" are numbers. This form is called slope-intercept because "m" is the slope and "b" is where the line crosses the y-axis. If two equations have the same "m" but different "b's," like y = 3x + 5 and y = 3x + 7, they are parallel -- same slope -- and cross the y-axis at different places.
Determine if the two lines cross at a right angle. Know that two lines cross at a right angle -- 90 degrees -- if the relationship between the slopes of the lines is m1 = -1/m2. Whenever the slopes of two lines are not equal, they will cross. If they cross at a 90-degree angle, the slope of one line is the negative reciprocal of the other line. If the first line has the formula y = 1/2x - 1 and the second line has the formula y = -2x + 3, the two lines cross each other at a right angle. If m1 = the slope of the first line and m2 = the slope of the second line, m1 = -1/m2 and m2 = -1/m1. In the example, -2 is the negative reciprocal of 1/2.