A total of 8 types of lines can be drawn on a Cartisean Plane in 2D. Following are they:
S.No | Diagram | Equation | Slope | Intercepts | Explanation |
---|---|---|---|---|---|
1. | \( x=C \) | Undefined | x Intercept=C y Intercept=Undefined |
These lines are perpendicular to X axis (and consequently parallel to Y axis). The line \(x=0\) is the Y axis. | |
2. | \( y=C \) | 0 | x Intercept=Undefined y Intercept=C |
These lines are perpendicular to Y axis (and consequently parallel to X axis). The line \(y=0\) is the X axis. | |
3. |
\( Ax-By=0 \) OR \( By=Ax \) |
\(\frac{A}{B}\) | x Intercept=0 y 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. | |
4. |
\( Ax+By=0 \) OR \( By=-Ax \) |
\(\frac{-A}{B}\) | x Intercept=0 y 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. | |
5. |
\(Ax+By+C=0\) 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. | |
6. |
\(Ax+By-C=0\) 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. | |
7. |
\(-Ax+By+C=0\) 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. | |
8. |
\(Ax-By+C=0\) 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. |