EQUATION OF A LINE

Methods for determining the equation of a line usually depend upon some knowledge of a point or points on the line.

An equation of a line is usually written in one of these forms:-

Ax + by + c = 0

Sometimes called the Standard form

Y = mx + b,

Where m is the slope and b is the y – intercept and is called the Slope intercept form
Any line that is not parallel to the Y axis intersects the Y axis at some point. The x coordinate of the point of intersection is 0, because the Y axis is vertical and passes through the origin. Let the y coordinate of the point of intersection be represented by b. Then the point of intersection is (O,b), as shown in figure 1-8. The y coordinate, b, is called the y intercept.

In point slope form we can write equation of a line through a point P(x1 , y1) with slope m is given by

y - y1 = m(x - x1)

The point-slope form may be used to find equation of a line through two known points

Find equation of a line that passes through the point (-2 , 5) and has a slope of -4

Substitute y1 , x1 and m in the point slope form of a line

y - y1 = m(x - x1) y - 5 = - 4(x - (-2)) y = - 4x - 3