•  
agra,ahmedabad,ajmer,akola,aligarh,ambala,amravati,amritsar,aurangabad,ayodhya,bangalore,bareilly,bathinda,bhagalpur,bhilai,bhiwani,bhopal,bhubaneswar,bikaner,bilaspur,bokaro,chandigarh,chennai,coimbatore,cuttack,dehradun,delhi ncr,dhanbad,dibrugarh,durgapur,faridabad,ferozpur,gandhinagar,gaya,ghaziabad,goa,gorakhpur,greater noida,gurugram,guwahati,gwalior,haldwani,haridwar,hisar,hyderabad,indore,jabalpur,jaipur,jalandhar,jammu,jamshedpur,jhansi,jodhpur,jorhat,kaithal,kanpur,karimnagar,karnal,kashipur,khammam,kharagpur,kochi,kolhapur,kolkata,kota,kottayam,kozhikode,kurnool,kurukshetra,latur,lucknow,ludhiana,madurai,mangaluru,mathura,meerut,moradabad,mumbai,muzaffarpur,mysore,nagpur,nanded,narnaul,nashik,nellore,noida,palwal,panchkula,panipat,pathankot,patiala,patna,prayagraj,puducherry,pune,raipur,rajahmundry,ranchi,rewa,rewari,rohtak,rudrapur,saharanpur,salem,secunderabad,silchar,siliguri,sirsa,solapur,sri-ganganagar,srinagar,surat,thrissur,tinsukia,tiruchirapalli,tirupati,trivandrum,udaipur,udhampur,ujjain,vadodara,vapi,varanasi,vellore,vijayawada,visakhapatnam,warangal,yamuna-nagar
General Equation of a Line

General Equation of a Line

Mathematically, we define a line as a two-dimensional figure without any width. If we need to join two points, we can join them with an infinite number of points. These points together form a line.

We can represent every line with an equation. We can represent every line with a universal equation, whether it is a curved line or a straight line. In this article, we will discuss the equation of a straight line.

Equation of a straight line

A straight line is a line which neither bends or twists. Examples of straight lines are rays of sunlight, beams of a candle, a ruler, etc. All these travel straight or exist straight in nature.

The universal equation of a straight line is given by: ax + by = c. We also represent the line as: y = mx + c. Here, m is the slope of the line, c is the intercept and x and y are the coordinates of the points along which the line must be drawn. This is known as the slope form of representing the equation of a line.

We can represent a line in various forms: slope-intercept form, general form, standard form, point-slope form, etc.

If we want to join two straight lines, then we need a line to join them. For example, suppose the coordinates of these points are P (x, y) and Q (n, m). Then we need a line to join these coordinates of points.

Forms of equations of a line

The slope is the angle formed between the line and the particular axis we need to construct the line. In other words, the slope is the inclination between a line with the x or y-axis.

One must note that the slopes of the x and y axes are 0 as they are always straight. Therefore, a line parallel to the x-axis will also have a zero slope, and a line parallel to the y axis will also have a zero slope.

Standard equation of a line

The standard equation of line: ax + by = c

Where a, b and c are real numbers.

Consider an equation of line 4x + 6 = 0. In this equation, a = 4, b = 0 and c = -6. Since we do not have any coefficient of y, therefore, the value of y is zero.

Point-slope form

We can find the equation of a line if we know the slope and coordinates of a point.

The point-slope form of the line is given by: y – y1 = m (x – x1).

Here, m is the slope of line

x, and y are the arbitrary points.

x1 and y1 are the coordinates of the point along which we need to draw the line.

Derivation of point-slope form

Let us consider a line with slope m, and a point with coordinates (x1, y1). We know,

Slope = difference in y coordinates / difference in x coordinates

m = (y – y1) / (x – x1)

Multiply both sides by (x – x1), we have,

m (x – x1) = (y – y1)

We can rewrite the above equation as (y – y1) = m (x – x1), the point-slope form.

Slope-intercept form

The slope-intercept form of a line: y = mx + c

Where m is the slope of the line

c is the intercept along the y axis

We can alternatively rewrite this equation as y = mx – d, where d is the x-intercept.

Equation of a line on a graph

We can represent a straight line on a graph by knowing the coordinates of the line. By using the equation ax + by = c, we can find multiple points of x and y and construct a line as shown:

 

Aakashians JEE Topper

Aakashians NEET UG 2023 Champions Again

Historic Results 2023 Aakashians Qualified +1 Lakh

JEE Advanced 2023

JEE Advanced 2023 Stats

JEE Advanced 2022 Topper

NEET Related Links

NEET Exam 2024

NEET 2024 Exam Dates

NEET 2024 Exam pattern

NEET 2024 Syllabus

NEET 2024 Eligibility Criteria

NEET 2024 Application

NEET UG Counselling

NEET FAQ

NEET UG Result

NEET 2024 Cut Off

Neet 2023 Toppers List Names & Rank

Neet Result 2023 Toppers list rank cut off

Neet Answer key Live Download PDF

Neet 2023 State Toppers List

JEE MAIN Related Links

JEE Main 2024

JEE Main Rank Predictor 2024

JEE Main College Predictor 2024

JEE Main 2024 Exam Dates

JEE Main 2024 Exam pattern

JEE Main 2024 Application

JEE Main 2024 Eligibility Criteria

JEE Main 2024 Syllabus

JEE Main 2024 Physics Syllabus

JEE Main 2024 Maths Syllabus

JEE Main 2024 Chemistry Syllabus

JEE Main 2024 Admit Card

JEE Main 2024 Counselling

JEE Main marks vs rank vs percentile

JEE Advanced Result 2023 live topper list

JEE Exam Preparation - How to calculate your rank jee

JEE Maths Syllabus - Important topics and weightage

JEE Advanced Related Links

JEE Advanced 2024 Exam Dates

JEE Advanced 2024 Application

JEE Advanced 2024 Eligibility Criteria

JEE Advanced 2024 Syllabus

JEE Advanced 2024 Maths Syllabus

JEE Advanced 2024 Physics Syllabus

JEE Advanced 2024 Chemistry Syllabus

JEE Advanced Exam Result

JEE Advanced Exam Dates

JEE Advanced Registration Dates

CUET Related Links

CUET 2024 Eligibility Criteria

CUET 2024 Admit Card

CUET 2024 Exam Pattern

CUET 2024 FAQs

CUET 2024 Counselling

CUET 2024 Syllabus

CUET 2024 Result

CUET 2024 Answer Key

CUET 2024 Preparation

CUET CUTOFF

CUET 2024 Application Form

Talk to our expert
Resend OTP Timer =
By submitting up, I agree to receive all the Whatsapp communication on my registered number and Aakash terms and conditions and privacy policy