# Types of Lines in 2D

A total of 8 types of lines can be drawn on a Cartisean Plane in 2D. Following are they:

S.No Diagram Equation Slope Explanation $$x=C$$ Undefined x Intercept=Cy Intercept=Undefined These lines are perpendicular to X axis (and consequently parallel to Y axis). The line $$x=0$$ is the Y axis. $$y=C$$ 0 x Intercept=Undefinedy Intercept=C These lines are perpendicular to Y axis (and consequently parallel to X axis). The line $$y=0$$ is the X axis. $$Ax-By=0$$ OR $$By=Ax$$ $$\frac{A}{B}$$ x Intercept=0y Intercept=0 These lines pass through the origin (0,0). The value of y increases with increase in x and decreases with decrease in x. Slope is positive. $$Ax+By=0$$ OR $$By=-Ax$$ $$\frac{-A}{B}$$ x Intercept=0y Intercept=0 These lines pass through the origin (0,0). The value of y decreases with increase in x and increases with decrease in x. Slope is negative. $$Ax+By+C=0$$ OR $$-Ax-By-C=0$$ $$\frac{-A}{B}$$ x Intercept=$$\frac{-C}{A}$$y Intercept=$$\frac{-C}{B}$$ In these lines both the coefficients A and B and the constant C have same sign on same side of the equation.The value of y decreases with increase in x and increases with decrease in x. Both x and y intercepts are negative. Slope is negative. $$Ax+By-C=0$$ OR $$-Ax-By+C=0$$ $$\frac{-A}{B}$$ x Intercept=$$\frac{C}{A}$$y Intercept=$$\frac{C}{B}$$ In these lines both the coefficients A and B have a different sign than the constanct C on same side of the equation. The value of y decreases with increase in x and increases with decrease in x. Both x and y intercepts are positive. Slope is negative. $$-Ax+By+C=0$$ OR $$Ax-By-C=0$$ $$\frac{A}{B}$$ x Intercept=$$\frac{C}{A}$$y Intercept=$$\frac{-C}{B}$$ In these lines the coefficient A has a different sign than coefficient B and constanct C on same side of the equation. The value of y increases with increase in x and decreases with decrease in x. X intercept is positive.Y intercept is negative. Slope is positive. $$Ax-By+C=0$$ OR $$-Ax+By-C=0$$ $$\frac{A}{B}$$ x Intercept=$$\frac{-C}{A}$$y Intercept=$$\frac{C}{B}$$ In these lines the coefficient B has a different sign than coefficient A and constanct C on same side of the equation. The value of y increases with increase in x and decreases with decrease in x. X intercept is negative. Y intercept is positive. Slope is positive.