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):

$$4x+2y+10=0$$

$$4x+2y+10-10=0-10$$

$$4x+2y=-10$$

$$4x+2y-4x=-4x-10$$

$$2y=-4x-10$$

$$y={\displaystyle \frac{-4x-10}{2}}$$

$$y={\displaystyle \frac{-4x}{2}}-{\displaystyle \frac{10}{2}}$$

$$y=-2x-5$$

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

- Everything needs to be pushed to one side, causing the equation to equal 0.
- 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:

$$y=-{\displaystyle \frac{1}{2}}x-5$$

$$y+{\displaystyle \frac{1}{2}}x+5=-{\displaystyle \frac{1}{2}}x-5+{\displaystyle \frac{1}{2}}x+5$$

$$y+{\displaystyle \frac{1}{2}}x+5=0$$

$$2y+{\displaystyle \frac{1}{2}}x+5=0$$

$$2y+x+10=0$$

- Last Updated: Oct 20, 2023 1:48 PM
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