How do you write an equation in slope-intercept form?

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To write an equation in slope-intercept form, you need to understand the basic structure of the equation, which is y = mx + b. In this equation:

  • y represents the dependent variable (the output).
  • x represents the independent variable (the input).
  • m is the slope of the line, which indicates how steep the line is and the direction it goes. A positive slope means the line rises as it moves to the right, while a negative slope means it falls.
  • b is the y-intercept, the point where the line crosses the y-axis (where x = 0).

To put an equation into this form, follow these steps:

  1. Start with the standard form of the equation (if given), which often looks like Ax + By = C.
  2. Isolate y on one side of the equation. You can do this by subtracting Ax from both sides:

    3. By = C – Ax

  3. Next, divide every term by B to solve for y:

    4. y = (-A/B)x + (C/B)

After simplifying, you will have your equation in the slope-intercept form y = mx + b, where:

  • The slope m is -A/B.
  • The y-intercept b is C/B.

For example, if you start with the equation 2x + 3y = 6:

  1. Subtract 2x from both sides: 3y = 6 – 2x.
  2. Divide everything by 3: y = (-2/3)x + 2.

Now, the equation is in slope-intercept form with a slope of -2/3 and a y-intercept of 2.

Using these steps, you can convert any linear equation into the slope-intercept form!

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