How to Graph Linear Equations Using the Intercepts Method

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There are many ways to graph a line: plugging in points, calculating the slope and y-intercept of a line, using a graphing calculator, etc. This article will teach you how to graph a line using intercepts.

Steps

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  1. Identify both. For the sake of clarity, let the independent be x and the dependent be y. [1]
  2. [2]
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  3. This will generate a coordinate for your y-intercept. First, substitute x to zero. Then, subtract the product from both sides of the equation. Note that the operation you will perform with both sides depends on the sign of your number. In this case the number is zero so we will use its opposite, subtraction. After that, divide three from both sides. And, VOILA! You have the answer. [3]
  4. (x,y) Since x=0, your coordinate pair will be similar to: (0,y).
  5. [4]
  6. Again, since you set y=0, your coordinate pair will look something like: (x,0).
  7. [5]
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  • Question
    Do we need to figure an equation out before knowing to change the x or y to 0, or can I change either/or in any equation?
    Elena Himmerich
    Community Answer
    You do need an equation to figure out an x- or y-intercept, but it doesn't need to be in any specific form. For example, you could just as easily change a variable to zero in a standard form equation as you could in a point-slope form equation.
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  • Question
    What if there is something attached to the equation? (E.g. y/2 = 10-4x)
    Technist
    Community Answer
    You can convert that into a linear equation like the one shown in the article. y/2 is the same as (1/2)y, so the coefficient is 1/2. You can also add 4x to both sides so that the equation is now 4x + (1/2)y = 10 and use the method shown in the article. By substituting 0 into x and then y, we get the intercepts (0, 20) and (5/2, 0). (Note: 5/2 = 2.5 so it doesn't matter which one you end up with.) You can then plot those two points and draw a straight line through both.
    Thanks! We're glad this was helpful.
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  • Question
    Can we take other values of x and y in table?
    Donagan
    Top Answerer
    Yes. A straight line is defined by two points. So if you're simply trying to graph a straight line, you can use any two pairs of coordinates (from the table) to find two points on the line. If, however, you want to use the intercepts method shown above, you would need to set either x or y equal to zero as shown in the article.
    Thanks! We're glad this was helpful.
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      References

      1. ↑ https://2012books.lardbucket.org/books/beginning-algebra/s06-03-graph-using-intercepts.html
      2. ↑ https://math.libretexts.org/Bookshelves/Algebra/Beginning_Algebra/03%3A_Graphing_Lines/3.03%3A_Graph_Using_Intercepts
      3. ↑ https://2012books.lardbucket.org/books/beginning-algebra/s06-03-graph-using-intercepts.html
      4. ↑ https://www.chilimath.com/lessons/intermediate-algebra/graph-a-line-using-x-and-y-intercepts/
      5. ↑ https://pressbooks.bccampus.ca/algebraintermediate/chapter/graph-linear-equations-in-two-variables/
      6. ↑ https://pressbooks.bccampus.ca/algebraintermediate/chapter/graph-linear-equations-in-two-variables/
      7. ↑ https://www.eduplace.com/math/mathsteps/4/c/index.html

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