Return to the Purplemath home page

 The Purplemath Forums
Helping students gain understanding
and self-confidence in algebra


powered by FreeFind

 

Return to the Lessons Index  | Do the Lessons in Order  |  Get "Purplemath on CD" for offline use  |  Print-friendly page

Solving "Ax + By = C" for "y=" (page 2 of 2)

Sections: Solving for a given variable, Solving for "y="


Probably one of the more important classes of literal equations you will need to solve will be linear equations. For instance, it is common that you are given problems of this type:

  • What is the slope of the line with equation 3x + 2y = 8?

    In order to find the slope, it is simplest to put this line equation into slope-intercept form. If I rearrange this line to be in the form "y = mx + b", it will be easy to read off the slope m. So I'll solve:

      3x + 2y = 8
      2y = 3x + 8

      y = ( 3/2 ) x + 4

    Then the slope is m3/2 .

Warning: There are many contexts, such as graphing and systems of equations, in which you will need to be able to solve a linear equation for "y =", so make sure you are comfortable with these techniques.

  • Find the slope and y-intercept of the line with equation 2x y = 5.

    I'll solve for "y =": Copyright Elizabeth Stapel 2002-2011 All Rights Reserved

     

    ADVERTISEMENT

     

      2x y = 5
      2x = y + 5

      2x 5 = y

    Then y = 2x 5, and, from the slope-intercept form of y = mx + b, I can see that:

      the slope is m = 2 and the y-intercept is b = 5.

  • Find the slope and y-intercept of the line with equation x 2y = 5.

    I'll solve for "y =":

      x 2y = 5
      x = 2y + 5

      x 5 = 2y

      ( 1/2 ) x ( 5/2 ) = y

    Then y = ( 1/2 ) x ( 5/2 ), so:

      the slope is m1/2  and the y-intercept is b5/2 .

  • Find the slope and y-intercept of the line with equation 4x + 5y = 12.

    I'll solve for "y =":

      4x + 5y = 12
      5y = 4x + 12

      y = ( 4/5 ) x + ( 12/5 )

    Then the slope is m4/5 and the y-intercept is b12/5 .


Don't let literal equations "throw" you. Solving literal equations is just like solving linear (and other sorts of) equations, except that the answers don't simplify as much. The techniques involved are otherwise exactly the same. Just take your time and be sure to write out all your steps clearly.

<< Previous  Top  |  1 | 2  |  Return to Index

Cite this article as:

Stapel, Elizabeth. "Solving 'Ax + By = C' for 'y='." Purplemath. Available from
    http://www.purplemath.com/modules/solvelit2.htm. Accessed
 

 



Purplemath:
  Linking to this site
  Printing pages
  School licensing


Reviews of
Internet Sites:
   Free Help
   Practice
   Et Cetera

The "Homework
   Guidelines"

Study Skills Survey

Tutoring from Purplemath
Find a local math tutor


This lesson may be printed out for your personal use.

Content copyright protected by Copyscape website plagiarism search

  Copyright 2002-2012  Elizabeth Stapel   |   About   |   Terms of Use

 

 Feedback   |   Error?