General form of the equation of a line

The equation of a straight line can be written in many different forms. One of the common forms is the general form.

Ax + By + C = 0

is the general form of the equation of a straight line

The following equations are in said to be in general form:

• x + 3y + 4 = 0
• 10x + 15y + 4 = 0
• x - 10y = 0 (here 'C' is zero)
• x + 3 = 0 (here 'B' is zero)
• 4y + 2 = 0 (here 'A' is zero)

An equation written in general form should not start with a negative number, that is, the value of the coefficient of x (represented by A) should not be a negative number.

The following equations are not in the general form:

• x + 3y = 4 (the number 4 should be on the left hand side)
• -x - 10y = 0 (x should not be negative)
• x + 3 + y = 0 (the correct order is x, then y then the number)

Some equations in the general form, with their graphs:

• x + 3y + 4 = 0

•  10x + 15y + 4 = 0 

Getting the x and y intercepts and slope from an equation in the general form

An equation written in the general form Ax + By + C = 0, has

• x-intercept = -C/A 

• y-intercept = -C/B

• slope = -A/B