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.

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  • Kelsen Miener

    7 years agoPosted 7 years ago. Direct link to Kelsen Miener's post “In the point slopes form,...”

    In the point slopes form, it looks like you're saying you could use either set of coordinates.I thought it was the first set of coordinates since it says x1 and y1. Please explain. Thanks.

    (19 votes)

    • Scott Ferguson

      4 years agoPosted 4 years ago. Direct link to Scott Ferguson's post “That is correct. You can ...”

      Forms of linear equations review (article) | Khan Academy (4)

      Forms of linear equations review (article) | Khan Academy (5)

      That is correct. You can definitely use either set of coordinates. Don't mix-and-match: you can't use x1 and y2, but you can use (x1, y1) or (x2, y2) and it will work just as well either way.

      (44 votes)

  • Betsy Glad

    3 years agoPosted 3 years ago. Direct link to Betsy Glad's post “How do you know when to u...”

    How do you know when to use point slope form vs slope intercept form?

    (16 votes)

  • ZetaFox

    3 years agoPosted 3 years ago. Direct link to ZetaFox's post “ax + by + c = 0ax + by =...”

    ax + by + c = 0
    ax + by = c

    I've heard of 2 "standard" forms of linear equations. Which one is correct?

    should c in the 1st line be -c though? since im moving it from the right to left...?

    (9 votes)

    • Khushi Viramgami

      3 years agoPosted 3 years ago. Direct link to Khushi Viramgami's post “hey! okay, so I'm pretty ...”

      Forms of linear equations review (article) | Khan Academy (13)

      hey! okay, so I'm pretty sure you're confusing a quadratic equation with a linear equation. A linear equation is a straight line, while a quadratic is a curve/parabola. You'll probably learn that later in algebra 1 and 2.

      anyways, the standard linear equation is ax+by=c, while the standard quadratic equation is slightly different from what you have; it should be ax^2+bx+c=0

      hope this helps!!

      (19 votes)

  • victoria.reed

    7 years agoPosted 7 years ago. Direct link to victoria.reed's post “when do you need to use s...”

    when do you need to use slope?

    (12 votes)

    • James Gallagher

      a year agoPosted a year ago. Direct link to James Gallagher's post “To determining the slope/...”

      To determining the slope/ steepness of a line. You should review the slope videos if you need help.

      (1 vote)

  • Corey Zuk

    3 years agoPosted 3 years ago. Direct link to Corey Zuk's post “i must be behind in math ...”

    i must be behind in math because all of this is way too confusing

    (10 votes)

  • mickycarey

    10 months agoPosted 10 months ago. Direct link to mickycarey's post “In the previous exercise:...”

    In the previous exercise: "Linear equations in any form", is there a method to figure out from the graph the equation in standard form directly or do you have to work out one of the slope forms first and then re-arrange the formula?

    (4 votes)

    • Kim Seidel

      10 months agoPosted 10 months ago. Direct link to Kim Seidel's post “You would need to use poi...”

      You would need to use point-slope form or slope intercept form to create an equation. Then, convert it to standard form.

      (7 votes)

  • worldsage

    7 years agoPosted 7 years ago. Direct link to worldsage's post “Is it possible to convert...”

    Is it possible to convert standard form back to point-slope directly?

    (5 votes)

  • em

    4 years agoPosted 4 years ago. Direct link to em's post “Why are point-slope opera...”

    Why are point-slope operations the opposite?
    For example, the point is (2,-3).
    why is y+3=3/4(x-2) correct but not y-3=3/4(x+2)?

    (3 votes)

    • Kim Seidel

      4 years agoPosted 4 years ago. Direct link to Kim Seidel's post “Point slope form is a var...”

      Point slope form is a variation of the slope formula:
      Slope m = (y2-y1)/(x2-x1)
      If you mulitply both sides by (x2-x1), then you get point slope form:
      (y2-y1) = m(x2-x1)
      Then, they swab a couple of variables to clarify the variables that stay. X2 becomes X, and Y2 becomes Y. And, you have the point slope form.

      Remember, slope is calculated as the change in Y over the change in X. So, it requires the subtraction.

      Hope this helps.

      (8 votes)

  • ultraidiotboy

    3 years agoPosted 3 years ago. Direct link to ultraidiotboy's post “what’s point-slope form g...”

    what’s point-slope form going to be useful for?

    (4 votes)

    • etoile~

      3 years agoPosted 3 years ago. Direct link to etoile~'s post “Point slope form is impor...”

      Point slope form is important because it can give us another set of coordinate pairs when we are only given one. Using algebraic manipulation, you can find coordinates and the slope from just that equation which helps with graphing. Being able to readily switch from different linear equation forms helps solving complex problems. Hope this helps. 🙃

      (6 votes)

  • Stelios Kourentzis

    4 years agoPosted 4 years ago. Direct link to Stelios Kourentzis's post “at the end it says this i...”

    at the end it says this is a standard form y+3x=−10
    it sould be fist 3x +y= -10 isn't ?

    (4 votes)

    • Peter Dresslar

      3 years agoPosted 3 years ago. Direct link to Peter Dresslar's post “Specifically there are a ...”

      Specifically there are a lot of teachers that would mark y+3x=−10 wrong. Maybe correctly; the form is the whole point of the exercise.

      (2 votes)

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

FAQs

What are the different forms of linear functions? ›

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

What are most linear equations written in? ›

The standard form for linear equations in two variables is Ax+By=C. For example, 2x+3y=5 is a linear equation in standard form. When an equation is given in this form, it's pretty easy to find both intercepts (x and y). This form is also very useful when solving systems of two linear equations.

How do you solve linear form? ›

To solve linear equations, find the value of the variable that makes the equation true. Use the inverse of the number that multiplies the variable, and multiply or divide both sides by it. Simplify the result to get the variable value. Check your answer by plugging it back into the equation.

What is standard form algebra? ›

The standard form equation is a way to write an equation by arranging the variables and the constant on the left of the equation. The standard form is written as Ax + By + C = 0 and can be used for any type of equation.

What are the forms of linear equation notes? ›

Notes
  • General Form. Ax+By+C=0. A, B, and C are simplified whole numbers. A is positive.
  • Standard Form. Ax+By=C. A, B, and C are simplified whole numbers. A is positive.
  • Slope Intercept Form. y=mx+b.
  • Point Slope Form. y-y_1=m(x-x_1) m=slope. (x_1.y_1) is any point on the line.

What are the different types of slope forms of linear equations? ›

Slopes come in 4 different types: negative, positive, zero, and undefined. as x increases. The slope of a line can also be interpreted as the “average rate of change”. It tells us how fast y is changing with respect to x.

How do you convert an equation to linear form? ›

Thus, to convert to general linear form, first isolate x and y on one side and the constant term on the other side. Next, if any of the coefficients are fractions, multiply the entire equation by the least common denominator of all the fractions. Example: Convert y + 1 = (x - 2) to general linear form.

What are 4 examples of linear equations? ›

Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3. In this article, we are going to discuss the definition of linear equations, standard form for linear equation in one variable, two variables, three variables and their examples with complete explanation.

How to do linear equations step by step? ›

The steps for solving linear equations are:
  1. Simplify both sides of the equation and combine all same-side like terms.
  2. Combine opposite-side like terms to obtain the variable term on one side of the equal sign and the constant term on the other.
  3. Divide or multiply as needed to isolate the variable.
  4. Check the answer.
Oct 6, 2021

What are the basics of linear equations? ›

The slope-intercept form of a linear equation is y = mx + b. In the equation, x and y are the variables. The numbers m and b give the slope of the line (m) and the value of y when x is 0 (b). The value of y when x is 0 is called the y-intercept because (0,y) is the point at which the line crosses the y-axis.

What is the slope intercept form of a linear equation? ›

Slope-intercept form (y=mx+b) of linear equations highlights the slope (m) and the y-intercept (b) of a line. Watch this video to learn more about it and see some examples.

What are the three different linear functions? ›

Linear functions: slope, intercept, and graph.

What are the 4 ways to represent a linear function? ›

There are several ways to represent a linear function, including word form, function notation, tabular form, and graphical form.

What are the different forms of linear systems? ›

Point Slope Form
Linear EquationGeneral FormExample
Slope intercept formy = mx + by + 2x = 3
Point–slope formy – y1 = m(x – x1 )y – 3 = 6(x – 2)
General FormAx + By + C = 02x + 3y – 6 = 0
Intercept formx/a + y/b = 1x/2 + y/3 = 1
3 more rows
Oct 31, 2020

What are the different representations of linear functions? ›

A linear function is a polynomial function of degree zero or one and a relationship that has a graph that makes a straight line. Relationships and functions can be represented as graphs, tables, equations, or verbal descriptions. Each representation gives us certain information.

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