There are many forms of the equation of a straight line. These are the slope-intercept form, the point-slope form and the two point form of the equation of a line.

Slope intercept form

y = mx + bIn the above form, 'm' represents the slope of the line, and 'b' represents the y-intercept of the line. Thus, if an equation is written in the slope intercept form, you can directly derive the slope and y-intercept from that equation by finding out the values of 'm' and 'b'.

Point slope form

y - y1 = m(x - x1)When the point through which a line passes, and its slope, are given in a question, then this form of the equation of a line is used to derive get the equation. In the above equation, 'x1' and 'y1' represent the coordinates of a point through which the line passes. Thus, (x1, y1) is the point through which the line passes. 'm', as above, represents the slope of the line.

Two point form

y - y1 = (y2 - y1)/(x2 -x1) * (x - x1)In this form of the equation of a line, 'x1', 'y1', 'x2' and 'y2' are the coordinates of two points (x1, y1) and (x2, y2). This equation is applied when the coordinates of two points through which a line passes are given in a question.

General form

Ax + By + C = 0This is the standard form of the equation of a line. The letters, A and B are the coefficients of x and y. C is the constant term. This form is commonly used to write down the resultant equation of a line in a question.