Select Page

Equation of a Line

The equation of a line is a linear relation between two variables x and y, which is satisfied by the coordinates of each & every point on the line and not by any other point.

There are various forms of Equation of a line.

equation of a line


  1. 2x + 3y + 7 = 0 which can also be written as 2x + 3y = (-7).
  2. 4x + 3 = 7 where B = 0.
  3. 3y + 2 = 5 where A = 0.
equation of a line

Point Slope Form

Equation of a line with slope or gradient m and passing through the point (x_{{1}},y_{{1}}) is given by

(y_{{}} – y_{{1}}) = m_{{}} (x_{{}} – x_{{1}})

equation of a line


  1. Equation of line passing from origin (0, 0) and slope 1 is (y – 0) = (x – 0) or y = x.
  2. Equation of line passing from (1, 3) and slope 4 is (y – 3) = 4(x – 1) or y – 3 = 4x – 4

Hence the line is given by the equation 4x – y – 1 = 0.


Slope Intercept form

The length of the intercept made by of a line on the Y-axis is called its y-intercept.

Equation of a line with slope or gradient m and making an y intercept of c units is given

by                                         (y – c) = m ( x – 0 )

i.e                                            y=mx + c

equation of a line
equation of a line


  1. Equation of line with slope, m = \frac{5}{{2}} &  y-intercept c = 7 is y =\frac{5}{{2}} x + 7.
  2. Equation of line with slope, m = 11 & y-intercept c = -2 is y = 11x – 2.
equation of a line
  1. Write the equation of the line 3x = 4y + 7 in general form.
  2. Convert the equation 3x = 4y + 2 in slope intercept form.
  3. Find the equation of the line passing from origin (0, 0) and slope 4.
  4. Find the equation of the line passing from origin (1, 5) and slope -7.
  5. Find the equation of the line with slope 2 & y-intercept 11.
  6. Find the equation of the line with slope \frac{3}{7} & y-intercept -5.
Answer key
  1. 3x – 4y – 7 = 0.
  2. Y =  \frac{3}{4} x  \frac{1}{2}
  3. y = 4x
  4. 7x + y – 12 = 0.
  5. y = 2x + 11
  6. y =  \frac{3}{7}x – 5 or 3x – 7y – 35=0.


Give Your Child The eTutorWorld Advantage

Research has proven that personal online tutoring not just cements school learning, it helps build student confidence. eTutorWorld provides the best K-12 Online Tutoring Services so you can learn from the comfort and safety of your home at an affordable cost.

Be it an exam, class test or a quiz, eTutorWorld’s Math, Science and English tutors are responsible for your academic progress. Meet your personal coach at your convenient day and time to get help for Grade 3-12 Math, Science and English subjects and AP, SAT, SSAT and SCAT Test Prep help and test practice. All our tutors are graduates and bring with them years of teaching experience to the tutoring lessons.

Our ‘Learning by Design’ methodology makes sure that each student is at the center of the teaching-learning process. All tutoring sessions start with a question to the student ‘What do you want to learn today?’ Hence, tutors diagnose your skills and recognize your requirements before the actual tutoring happens. Post every tutoring session, an individualized worksheet is emailed to the student to assimilate learned concepts. Regular formative assessments are used to evaluate a student’s understanding of the subject.

The state of the art technology used is stable, user friendly and safe. All you need is a computer or a tablet and an internet connection. The easy-to-use web conferencing software requires a one time download, using which the student can talk and chat to the tutor, annotate on an interactive shared whiteboard or even share documents, assignments or worksheets.

All tutoring sessions are recorded and made available for a month so you can review concepts taught.

Email or call our support team with any issues or questions – we are here for you 24X7.

Also, download free printable math and science worksheets in pdf format and solve SCAT and SSAT Practice Tests online. Sign up for a Free Trial Lesson Today!

Thousands have taken the eTutorWorld Advantage – what are you waiting for?

© 2019 eTutorWorld - Online Tutoring and Test Prep | All rights reserved

10% Discount on all Tutoring & Worksheet Packs

use coupon HALO10

You have Successfully Subscribed!