
A line passes through the point \((3,4)\) and cuts off intercepts from the coordinates axes such that their sum is \[14\]. The equation of the line is
A) \[4x - 3y = 24\]
B) \[\;\;4x + 3y = 24\]
C) \[\;3x - 4y = 24\]
D) \[\;3x + 4y = 24\]
Answer
162.3k+ views
Hint: Straight line is a set of infinites points in which all points are linear. Intercept is a point where a line cuts the x or y axis. In this question we have to find the equation of line which intercept equally on both axes. As intercept is given in this question therefore equation of the intercept form of straight line will be used in this question. Points lying on particular lines must satisfy the equation of the line.
Formula Used:In this question equation of intercept form of straight line is used:
\(\dfrac{x}{a} + \dfrac{y}{b} = 1\)
Where,
a and b are intercept of x and y axis respectively
Complete step by step solution:Given : straight line passes through the point \((3,4)\) and intercept are equal.
The equation of intercept form of straight line is
\(\dfrac{x}{a} + \dfrac{y}{b} = 1\)
a and b are intercept of x and y axis respectively
According to question intercept are equal
\[a + b = 14\]
Equation of required line
\(\dfrac{x}{{14 - b}} + \dfrac{y}{b} = 1\)
Now this lines passes through \((3,4)\)so this coordinate must satisfy the equation of line
\(\dfrac{3}{{14 - b}} + \dfrac{4}{b} = 1\)
\(3b + 56 - 4b = (14 - b)b\)
On simplification
\(b = 7\)Or \(b = 8\)
Equation of required line is:
When \(b = 7\)
\(\dfrac{x}{7} + \dfrac{y}{7} = 1\)
\(x + y = 7\)
When \(b = 8\)
\(\dfrac{x}{6} + \dfrac{y}{8} = 1\)
\[4x + 3y = 24\]
Option ‘B’ is correct
Note: Do not use the equation of line in any other form because it will become very difficult to find the equation of lines and sometimes one may not find the equation of line by using the general equation of lines. If in any question an intercept on line is given then use only the intercept form of the straight line equation.
Formula Used:In this question equation of intercept form of straight line is used:
\(\dfrac{x}{a} + \dfrac{y}{b} = 1\)
Where,
a and b are intercept of x and y axis respectively
Complete step by step solution:Given : straight line passes through the point \((3,4)\) and intercept are equal.
The equation of intercept form of straight line is
\(\dfrac{x}{a} + \dfrac{y}{b} = 1\)
a and b are intercept of x and y axis respectively
According to question intercept are equal
\[a + b = 14\]
Equation of required line
\(\dfrac{x}{{14 - b}} + \dfrac{y}{b} = 1\)
Now this lines passes through \((3,4)\)so this coordinate must satisfy the equation of line
\(\dfrac{3}{{14 - b}} + \dfrac{4}{b} = 1\)
\(3b + 56 - 4b = (14 - b)b\)
On simplification
\(b = 7\)Or \(b = 8\)
Equation of required line is:
When \(b = 7\)
\(\dfrac{x}{7} + \dfrac{y}{7} = 1\)
\(x + y = 7\)
When \(b = 8\)
\(\dfrac{x}{6} + \dfrac{y}{8} = 1\)
\[4x + 3y = 24\]
Option ‘B’ is correct
Note: Do not use the equation of line in any other form because it will become very difficult to find the equation of lines and sometimes one may not find the equation of line by using the general equation of lines. If in any question an intercept on line is given then use only the intercept form of the straight line equation.
Recently Updated Pages
If tan 1y tan 1x + tan 1left frac2x1 x2 right where x frac1sqrt 3 Then the value of y is

Geometry of Complex Numbers – Topics, Reception, Audience and Related Readings

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Electricity and Magnetism Important Concepts and Tips for Exam Preparation

JEE Energetics Important Concepts and Tips for Exam Preparation

Trending doubts
JEE Main 2025 Session 2: Application Form (Out), Exam Dates (Released), Eligibility, & More

JEE Main 2025: Derivation of Equation of Trajectory in Physics

Displacement-Time Graph and Velocity-Time Graph for JEE

Electric Field Due to Uniformly Charged Ring for JEE Main 2025 - Formula and Derivation

JoSAA JEE Main & Advanced 2025 Counselling: Registration Dates, Documents, Fees, Seat Allotment & Cut‑offs

NIT Cutoff Percentile for 2025

Other Pages
JEE Advanced Marks vs Ranks 2025: Understanding Category-wise Qualifying Marks and Previous Year Cut-offs

JEE Advanced Weightage 2025 Chapter-Wise for Physics, Maths and Chemistry

JEE Advanced 2025: Dates, Registration, Syllabus, Eligibility Criteria and More

Degree of Dissociation and Its Formula With Solved Example for JEE

Free Radical Substitution Mechanism of Alkanes for JEE Main 2025

JEE Advanced 2025 Notes
