Convert Standard Form to Slope-Intercept Form

Goal

Convert an equation from standard form into slope-intercept form: [ Ax+By=C \quad \rightarrow \quad y=mx+b ] In slope-intercept form, the coefficient of (x) is the slope, and the constant term is the y-intercept.

Method

1. Start with the standard-form equation. Write it exactly as given.

2. Isolate the (y)-term. Move the (x)-term and any constant terms to the other side using inverse operations.

3. Divide if needed. If the coefficient of (y) is not 1, divide every term by that coefficient.

4. Simplify. Reduce fractions, signs, and arithmetic so the equation is in the form (y=mx+b).

Example pattern

If you have something like (Ax+By=C), subtract (Ax) from both sides: [ By=-Ax+C ] Then divide by (B): [ y=-\frac{A}{B}x+\frac{C}{B} ]

Check your work

• The final equation should begin with (y=).
• Make sure the (x)-term and constant are both simplified.
• You can verify by substituting a point from the original equation, if one is available.