Find the equation of the line passing through the point (2, 3) and perpendicular to the line 4x + 3y = 10
Given: The given line is $4 x+3 y=10$. The line perpendicular to this line passes through $(2,3)$.
Formula to be used: The product of slopes of two perpendicular lines = - 1
Slope of this line is $-4 / 3$.
$\therefore$ the slope of the perpendicular line $=\frac{-1}{-4 / 3}=3 / 4$.
The equation of the line can be written in the form $y=\left(\frac{3}{4}\right) x+c$
(c is the y - intercept)
This line passes through (2,3), so the point will satisfy the equation of the line.
$\therefore 3=\left(\frac{3}{4}\right) \times 2+$ ci.e.c $=3-\frac{3}{2}=\frac{3}{2}$
The required equation is
$y=\frac{3}{4} x+\frac{3}{2}$
or, 4y = 3x + 6 i.e. 3x - 4y + 6 = 0.
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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,