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How to Convert a Slope-Intercept Form Equation Into a General Linear Equation

When writing linear equations, you can use either the slope-intercept form or general form. The advantage of slope-intercept form, or y = mx + b, is that you can immediately see the slope, m, and the y-intercept, b, just from looking at the equation. With the general form, Ax + By + C = 0, you can find both the x-intercept and y-intercept easily. In some cases, you will want to convert from the slope-intercept form to the general form, such as if your textbook or teacher requires you to report your answer in general form.

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Instructions

- 1
  Subtract the coefficient of x times x from both sides. For example, if your slope-intercept form equation is y = -4/7x + 2, subtract -4/7x from both sides of the equation to get 4/7x + y = 2.
- 2
  Subtract the y-intercept, the number without a coefficient, from both sides. In this example, subtract 2 from both sides to get 4/7x + y - 2 = 0.
- 3
  Multiply each term by the denominator of the x-coefficient, if any, to complete the conversion to general form. In this example, the x-coefficient equals 4/7, so 7 is the denominator. Therefore, multiply 7 by 4/7x, y, 2 and 0 to get (4/7x)*7 + y*7 - 2*7 = 0*7, which simplifies to 4x + 7y - 14 = 0.

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