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Graphing Linear Equations: More Examples (page 4 of 4)

Sections: Making a T-chart, Plotting the points and drawing the line, Examples

  • Graph x = 4   Copyright Elizabeth Stapel 2000-2011 All Rights Reserved
  • Don't let this one scare you either! Yes, there is no y in the equation, so you can't solve for
    y =", but that's okay. The reasoning works just like the previous example. No matter what y might happen to be, x is always 4.

    You'll do the T-chart backwards, picking various y-values and putting "4" as the corresponding x-values:




    Then the graph fills in like this:


    x = 4

Any time you have an "x equals a number" equation, with no y in it, the graph will always be a vertical line like this.

  • Graph 4x 3y = 12
  • For this example, it's simplest to first solve for "y =". This is especially true if you're using a graphing calculator, because graphing calculators can only handle "y =".

      4x - 3y = 12, then y = (4/3)x - 4

    So you're actually graphing this equation:


     y = (4/3)x - 4

    Since you are going to be multiplying your x-values by a fraction, it is simplest to pick x-values that are multiples of 3, so the denominator will cancel out.


    Here's the T-chart...






    ...and here's the graph:


     y = (4/3)x - 4

  • Graph 3x = 6y 2
    Solve first for "
    y =":


    -3x = 6y - 2, then -(1/2)x + 1/3 = y

    y = -(1/2)x + (1/3)


    Okay, so computing the plot points for this one is going to be messy, what with all the fractions. Do the best you can for the T-chart, remembering that you'll be rounding values when you go to plot the points:






    Draw the graph:


    y = -(1/2)x + (1/3)

Note that this graph needed to be larger than what I've drawn before. That's because the points were "messy", so I needed more points, and further apart, to make sure the line was right. Take the time to be careful!

There are other methods for graphing straight lines, such as graphing from the intercepts or graphing from the y-intercept and the slope. You should expect to be required to be able to use any method that has been introduced in your class.

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Cite this article as:

Stapel, Elizabeth. "Graphing Linear Equations: More Examples." Purplemath. Available from Accessed


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