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.NoDiagramEquationSlopeInterceptsExplanation
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.