IIT-JEE 2012-13 Series

Equation of a Line in Intercept Form

• The intercept form of a line's equation is represented as ( \frac{x}{a} + \frac{y}{b} = 1 ), where ( a ) is the x-intercept and ( b ) is the y-intercept.

Equation of a Constant Function

• A constant function is expressed as ( y = c ), where ( c ) is a constant value. This indicates a horizontal line at the y-value ( c ).

Equation of a Line Through a Given Point

• The equation for a line through a point ( (x_1, y_1) ) with slope ( m ) is given by the point-slope form: ( y - y_1 = m(x - x_1) ).

Equation of a Line with Slope and Intercept

• A line with slope ( m ) and y-intercept ( c ) can be formulated as ( y = mx + c ), indicating its vertical rise over horizontal run combined with the vertical displacement.

Equation of a Line in Standard Form

• The standard form of a line's equation is defined as ( Ax + By = C ), where ( A ), ( B ), and ( C ) are integers, and ( A ) is non-negative.

Reiteration of Key Equations

• A line with slope ( m ) and y-intercept ( c ) is reiterated as ( y = mx + c ).
• Standard form is again presented as ( Ax + By = C ).

Summary of Constant Functions

• The constant function previously defined reinforces the equation ( y = c ) as a representation of a horizontal line, emphasizing its characteristics of having no slope.