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Module 8: Linear Equations and Linear Systems

Converting between Both Forms

Much like fractions and decimals, both forms of representation are interconvertible. As previously mentioned, using slope-intercept is way more convenient for graphing purposes than standard form, which does not give any immediate hints in that regard.

Tutorial 31: How to Convert from Standard to Slope-Intercept

Converting from Standard to Slope-intercept is a matter of isolating the y variable from the rest of the equation. In other words, keep the y variable where it is and move the rest across the equal sign. Remember to work in reverse BEDMAS order (SAMDEB). If needed, refer to Tutorial 30 in the Isolation (Solving for a Variable) section in Module 7: Algebra for assistance.

Here is an example (full version):

4 x + 2 y + 10 = 0 {"version":"1.1","math":"4x+2y+10=0 "}

4 x + 2 y + 10 − 10 = 0 − 10 {"version":"1.1","math":"4x+2y+10−10=0−10 "}

4 x + 2 y = − 10 {"version":"1.1","math":"4x+2y=−10 "}

4 x + 2 y − 4 x = − 4 x − 10 {"version":"1.1","math":"4x+2y−4x=−4x−10 "}

2 y = − 4 x − 10 {"version":"1.1","math":"2y=−4x−10 "}

y = − 4 x − 10 2 {"version":"1.1","math":"y=\dfrac{-4x-10}{2}"}

y = − 4 x 2 − 10 2 {"version":"1.1","math":"y=\dfrac{-4x}{2}-\dfrac{10}{2}"}

y = − 2 x − 5 {"version":"1.1","math":"y=−2x−5 "}

Tutorial 32: How to Convert from Slope-Intercept to Standard Form

There are two keys to converting from slope-intercept to standard form.

  1. Everything needs to be pushed to one side, causing the equation to equal 0.
  2. No fractions allowed.

Make use of moving terms across an equal sign (Refer to Tutorial 30 in the Isolation (Solving for a Variable) section in Module 7: Algebra). In the event that you need to remove fractions, you must find a common multiple between every denominator and multiply it to every term in the equation. This will cancel out the denominators.

Here is an example:

y = − 1 2 x − 5 {"version":"1.1","math":"y=-\dfrac{1}{2}x-5"}

y + 1 2 x + 5 = − 1 2 x − 5 + 1 2 x + 5 {"version":"1.1","math":"y+\dfrac{1}{2}x+5=-\dfrac{1}{2}x-5+\dfrac{1}{2}x+5 "}

y + 1 2 x + 5 = 0 {"version":"1.1","math":"y+\dfrac{1}{2}x+5=0"}

2 y + 1 2 x + 5 = 0 {"version":"1.1","math":"2y+\dfrac{1}{2}x+5=0 "}

2 y + x + 10 = 0 {"version":"1.1","math":"2y+x+10=0 "}

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