The general equation of straight line is given by:
Ax + By = C
where A, B and C are constants and A and B cannot be both zero.
For an interactive exploration of this equation Go here.
Any straight line in a rectangular system has an equation
of the form given above.
Slope intercept form of a Line:
The equation of a line with a defined slope m can also be written as follows:
y = mx + b
where m is the slope of the line and b is the y intercept of the graph of the line.
The above form is called the slope intercept form of a line. To understand why, go to this interactive tutorial.
Point-Slope form of a line:
An equation of a line through a point P(x1 , y1)
with slope m is given by
y - y1 = m(x - x1)
Vertical and Horizontal lines:
a - If we set A to zero in the general equation, we obtain an equation in y only of the form
By = C
which gives y = C/B = k; k is a constant. This is a horizontal line with slope 0 and passes through all points with y coordinate equal to k.
b - If we set B to zero in the general equation, we obtain
Ax = C
which gives x = C/A = h; h is constant. This is a vertical line with undefined slope and passes through all points with x coordinate equal to h.
Two non vertical lines are parallel if and only if their
slopes are equal.
Two non vertical lines are perpendicular if and only if
their slopes m1 and m2 are such that
m1*m2 = -1
Example 1: Find the slope of a line passing
through the points