Straight Lines

Linear equations can be rewritten using the laws of elementary algebra into several different forms. These equations are often referred to as the “equations of the straight line.” In the general form the linear equation is written as: ax + by + c = ( . ) where a and b are not both equal to zero. The name “linear” comes from the fact that the set of solutions of such an equation forms a straight line in the plane.

In this chapter “line”, we mean a straight line unless otherwise stated. There are many ways to write the equation of a line which can all be converted from one to another by algebraic manipulation. These forms are generally named by the type of information (data) about the line that is needed to write down the form. Some of the important data are points, slope , and intercepts .

. The relationship between the angle of inclination and slope Definition . The angle of inclination of a straight line is the angle, say θ , made by the line with the x -axis measured in the counter clockwise (positive) direction.