Find the equation of the line

You can see the effect of different values of m (the slope) and b (the y intercept) at Explore the Straight Line Graph

Table of Contents Show

Other Forms
Country Note:
What are the 3 equations of a line?
How do you find the equation of a line that passes through a point?

Other Forms

We have been looking at the "slope-intercept" form. The equation of a straight line can be written in many other ways.

Another popular form is the Point-Slope Equation of a Straight Line.

358,359,517,518, 1156, 1157, 3204, 3205, 3206, 3207

Footnote

Country Note:

Different Countries teach different "notation" (as sent to me by kind readers):

In the US, Australia, Canada, Eritrea, Iran, Mexico, Portugal, Philippines and Saudi Arabia the notation is:y = mx + bIn the UK, Australia (also), Bahamas, Bangladesh, Belgium, Brunei, Bulgaria, Cyprus, Egypt, Germany, Ghana, India, Indonesia, Ireland, Jamaica, Kenya, Kuwait, Malaysia, Malawi, Malta, Nepal, New Zealand, Nigeria, Oman, Pakistan, Peru, Singapore, Solomon Islands, South Africa, Sri Lanka, Turkey, UAE, Zambia and Zimbabwey = mx + cIn Afghanistan, Albania, Algeria, Brazil, China, Czech Republic, Denmark, Ethiopia, France, Lebanon, Netherlands, Kosovo, Kyrgyzstan, Norway, Poland, Romania, South Korea, Surinam, Spain, Tunisia and Viet Nam:y = ax + bIn Azerbaijan, China, Finland, Russia and Ukraine:y = kx + bIn Greece:ψ = αχ + βIn Italy:y = mx + qIn Japan:y = mx + dIn Cuba and Israel:y = mx + nIn Romania:y = gA + CIn Latvia and Sweden:y = kx + mIn Serbia and Slovenia:y = kx + n In your country:let us know!

... but it all means the same thing, just different letters.

Slope (Gradient) of a Straight Line Y Intercept of a Straight Line Test Yourself Explore the Straight Line Graph Straight Line Graph Calculator Graph Index

To find the equation of a line using 2 points, start by finding the slope of the line by plugging the 2 sets of coordinates into the formula for slope. Then, plug the slope into the slope-intercept formula, or y = mx + b, where "m" is the slope and "x" and "y" are one set of coordinates on the line. Next, solve the formula to find the value of "b," which is the y-intercept. Finally, plug the slope and y-intercept into the slope-intercept formula to finish the equation of the line. To learn how to find the equation of a line using 1 point, scroll down!

Did this summary help you?YesNo

Thanks to all authors for creating a page that has been read 903,913 times.

If you know two points that a line passes through, this page will show you how to find the equation of the line.

Fill in one of the points that the line passes through...

( , )
Example: (3,2)

and the other point...

( , )
Example: (7,-4)

If you believe that content available by means of the Website (as defined in our Terms of Service) infringes one or more of your copyrights, please notify us by providing a written notice (“Infringement Notice”) containing the information described below to the designated agent listed below. If Varsity Tutors takes action in response to an Infringement Notice, it will make a good faith attempt to contact the party that made such content available by means of the most recent email address, if any, provided by such party to Varsity Tutors.

Your Infringement Notice may be forwarded to the party that made the content available or to third parties such as ChillingEffects.org.

Please be advised that you will be liable for damages (including costs and attorneys’ fees) if you materially misrepresent that a product or activity is infringing your copyrights. Thus, if you are not sure content located on or linked-to by the Website infringes your copyright, you should consider first contacting an attorney.

Please follow these steps to file a notice:

You must include the following:

A physical or electronic signature of the copyright owner or a person authorized to act on their behalf; An identification of the copyright claimed to have been infringed; A description of the nature and exact location of the content that you claim to infringe your copyright, in \ sufficient detail to permit Varsity Tutors to find and positively identify that content; for example we require a link to the specific question (not just the name of the question) that contains the content and a description of which specific portion of the question – an image, a link, the text, etc – your complaint refers to; Your name, address, telephone number and email address; and A statement by you: (a) that you believe in good faith that the use of the content that you claim to infringe your copyright is not authorized by law, or by the copyright owner or such owner’s agent; (b) that all of the information contained in your Infringement Notice is accurate, and (c) under penalty of perjury, that you are either the copyright owner or a person authorized to act on their behalf.