How Do You Change Standard Form into Slope-Intercept Form?

To change a linear equation from standard form to slope-intercept form, which is expressed as y = mx + b, follow these steps:

1. Start with the standard form equation: Standard form is typically written as Ax + By = C, where A, B, and C are constants.
2. Isolate the y term: To do this, subtract Ax from both sides of the equation:

By = C - Ax

3. Divide by B: This will give you y alone on one side:

y = -\frac{A}{B}x + \frac{C}{B}

4. Identify the slope and y-intercept: In the slope-intercept form y = mx + b, m is the slope and b is the y-intercept. Here, -\frac{A}{B} is the slope, and \frac{C}{B} is the y-intercept.

For example, let’s take the equation in standard form: 2x + 3y = 6. By following these steps:

1. Subtract 2x from both sides: 3y = 6 – 2x
2. Then divide everything by 3: y = -\frac{2}{3}x + 2

In this case, the slope is -\frac{2}{3} and the y-intercept is 2. Therefore, the equation in slope-intercept form is y = -\frac{2}{3}x + 2.