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IIT-JEE 2012-13 Series

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Questions and Answers

What is the equation of a line in intercept form?

$y = mx + c$ where $m$ is the slope and $c$ is the intercept on the $y$-axis

$\frac{x}{a} + \frac{y}{b} = 1$ where $a$ and $b$ are intercepts on the axes of $x$ and $y$ respectively (correct)

$y = h$ where $h$ is a constant

$y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a given point and $m$ is the slope

What is the equation of a constant function?

$y = h$ where $h$ is a constant (correct)

$y = mx + c$ where $m$ is the slope and $c$ is the intercept on the $y$-axis

$\frac{x}{a} + \frac{y}{b} = 1$ where $a$ and $b$ are intercepts on the axes of $x$ and $y$ respectively

$y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a given point and $m$ is the slope

What is the equation of a line through a given point $(x_1, y_1)$ with slope $m$?

$\frac{x}{a} + \frac{y}{b} = 1$ where $a$ and $b$ are intercepts on the axes of $x$ and $y$ respectively

$y = h$ where $h$ is a constant

$y = mx + c$ where $m$ is the slope and $c$ is the intercept on the $y$-axis

$y - y_1 = m(x - x_1)$ (correct)

What is the equation of a line with slope $m$ and intercept $c$ on the $y$-axis?

$y = mx + c$ where $m$ is the slope and $c$ is the intercept on the $y$-axis Signup and view all the answers

What is the equation for a line in standard form?

$y = mx + c$ where $m$ is the slope and $c$ is the intercept on the $y$-axis Signup and view all the answers

What is the equation of a line with slope $m$ and intercept $c$ on the $y$-axis?

$y = mx + c$ Signup and view all the answers

What is the equation of a line in standard form?

$ax + by = c$ Signup and view all the answers

What is the equation of a constant function?

$y = k$ Signup and view all the answers

What is the equation of a line through a given point $(x_1, y_1)$ with slope $m$?

$y - y_1 = m(x - x_1)$ Signup and view all the answers

What is the equation of a line in intercept form?

$\frac{x}{a} + \frac{y}{b} = 1$ Signup and view all the answers

Study Notes

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.

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Description

Test your knowledge of elementary algebra, polynomial equations, trigonometry, and functions with this IIT-JEE 2012-13 series quiz. Brush up on common formulae, binomial theorem, and trigonometric ratios to prepare for the exam.