Reduce the following equations into intercept form and find their intercepts on the axes.
(i) $3 x+2 y-12=0$
(ii) $4 x-3 y=6$
(iii) $3 y+2=0$.
(i) The given equation is 3x + 2y – 12 = 0.
It can be written as
$3 x+2 y=12$
$\frac{3 x}{12}+\frac{2 y}{12}=1$
i.e., $\frac{x}{4}+\frac{y}{6}=1$ $\ldots(1)$
This equation is of the form $\frac{x}{a}+\frac{y}{b}=1$, where $a=4$ and $b=6$.
(ii) The given equation is 4x – 3y = 6.
It can be written as
$\frac{4 x}{6}-\frac{3 y}{6}=1$
$\frac{2 x}{3}-\frac{y}{2}=1$
i.e., $\frac{x}{\left(\frac{3}{2}\right)}+\frac{y}{(-2)}=1$ $\ldots(2)$
This equation is of the form $\frac{x}{a}+\frac{y}{b}=1$, where $a=\frac{3}{2}$ and $b=-2$.
Therefore, equation (2) is in the intercept form, where the intercepts on the $x$ and $y$ axes are $\frac{3}{2}$ and $-2$ respectively.
(iii) The given equation is $3 y+2=0$.
It can be written as
$3 y=-2$
i.e., $\frac{y}{\left(-\frac{2}{3}\right)}=1$ $\ldots(3)$
This equation is of the form $\frac{x}{a}+\frac{y}{b}=1$, where $a=0$ and $b=-\frac{2}{3}$.
Therefore, equation (3) is in the intercept form, where the intercept on the $y$-axis is $-\frac{2}{3}$ and it has no intercept on the $x$-axis.
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All Study Material
- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,