Equation of a Line in Cartesian Plane

Equation of a line can be represented in many ways, few of which is given below-

(i) General Form

The general form of a line is given as Ax + By + C = 0.

(ii) Slope intercept Form 

Let x, y be the coordinate of a point through which a line passes, m be the slope of a line, and c be the y-intercept, then the equation of a line is given by:

y=mx + c

(iii) Intercept Form of a Line

Consider a and b be the x-intercept and y-intercept respectively, of a line, then the equation of a line is represented as-

y = mx + c

Slope of a Line: 

Consider the general form of a line Ax + By + C = 0, the slope can be found by converting this form to the slope-intercept form.

Ax + By + C = 0

⇒ By = − Ax – C

or,⇒�=−��⁢�–��

Comparing the above equation with y = mx + c,�=−��

Thus, we can directly find the slope of a line from the general equation of a line.

Coordinate Geometry Formulas and Theorems

Distance Formula: To Calculate Distance Between Two Points

Let the two points be A and B, having coordinates to be (x₁, y₁) and (x₂, y₂), respectively.

Thus, the distance between two points is given as-�=(�2−�1)2+(�2–�1)2

Coordinate Geometry Fig. 2: Distance Formula