Forms of linear equations review (article) | Khan Academy (2024)

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form. We review all three in this article.

Want to join the conversation?

Certainly! The concepts revolving around linear equations include various forms used for different purposes in mathematics. Let's dive into the specifics mentioned in the discussion and provide insights into each concept:

1. Point-Slope Form:

  • Description: Point-slope form is expressed as (y - y_1 = m(x - x_1)), where (m) represents the slope of the line, and ((x_1, y_1)) denotes a point on the line.
  • Insights from the Discussion:
    • Kelsen Miener and Scott Ferguson: Address the interchangeable use of coordinates ((x_1, y_1)) or ((x_2, y_2)) in the point-slope form.
    • em: Discusses the reversal of operations in point-slope equations, exemplifying how (y+3 = \frac{3}{4}(x-2)) is correct while (y-3 = \frac{3}{4}(x+2)) is not due to the opposite nature of operations.

2. Slope-Intercept Form:

  • Description: Slope-intercept form appears as (y = mx + b), where (m) signifies the slope, and (b) denotes the y-intercept.
  • Insights from the Discussion:
    • Betsy Glad and Kim Seidel: Inquire about choosing between point-slope and slope-intercept forms, highlighting that often, it's a matter of choice or might be specified by a teacher for particular exercises.

3. Standard Form:

  • Description: Standard form is represented as (Ax + By = C), where (A), (B), and (C) are constants, and (A) is non-negative.
  • Insights from the Discussion:
    • ZetaFox, Khushi Viramgami, Stelios Kourentzis, Peter Dresslar, and mickycarey: Engage in discussions and queries regarding the correctness of standard form equations, sign placement, and rearrangement of terms.

Additional Insights:

  • Use of Slope:
    • victoria.reed and James Gallagher: Address the use of slope in determining the steepness of a line and its importance in understanding linear equations.
  • Utility of Point-Slope Form:
    • etoile~: Highlights the significance of point-slope form in determining coordinates and slopes from a given equation, aiding in graphing and problem-solving.

Conversions and Relations:

  • Reverting from Standard Form to Point-Slope:
    • worldsage: Raises the query of converting standard form back to point-slope directly, indicating a desire to understand the interconvertibility of different linear equation forms.


The conversation showcases queries, clarifications, and discussions regarding the use, understanding, and interrelations among point-slope, slope-intercept, and standard forms of linear equations. It also emphasizes the practical applications, choices in usage, and the significance of slope in comprehending linear relationships and graphing.

Forms of linear equations review (article) | Khan Academy (2024)


Top Articles
Latest Posts
Article information

Author: Rob Wisoky

Last Updated:

Views: 5241

Rating: 4.8 / 5 (48 voted)

Reviews: 87% of readers found this page helpful

Author information

Name: Rob Wisoky

Birthday: 1994-09-30

Address: 5789 Michel Vista, West Domenic, OR 80464-9452

Phone: +97313824072371

Job: Education Orchestrator

Hobby: Lockpicking, Crocheting, Baton twirling, Video gaming, Jogging, Whittling, Model building

Introduction: My name is Rob Wisoky, I am a smiling, helpful, encouraging, zealous, energetic, faithful, fantastic person who loves writing and wants to share my knowledge and understanding with you.