Standard Form to Slope Intercept Form Calculator

A linear equation in standard form is written as Ax + By = C, where A, B, and C are integers, and A is typically non-negative. To convert this into slope-intercept form—expressed as y = mx + b—you must isolate the dependent variable y on the left side of the equation. First, subtract Ax from both sides to move the x-term: By = -Ax + C. Next, divide every term in the equation by coefficient B. This yields the slope-intercept form where the slope m = -A/B and the y-intercept b = C/B. If you are converting in reverse from slope-intercept to standard form, you clear fractions and rearrange terms so that both variables sit on the left side while the constant remains on the right.

Let us convert the standard form equation 3x + 4y = 12 into slope-intercept form. Here, our coefficients are A = 3, B = 4, and C = 12. First, isolate the y-term by subtracting 3x from both sides: 4y = -3x + 12. Then, divide all terms by the y-coefficient 4 to fully isolate y: y = (-3/4)x + 12/4. Simplifying the constant term gives us the final slope-intercept equation: y = -0.75x + 3. Thus, the slope is -0.75 and the y-intercept is 3.

When working with linear equations, always check that your coefficient B is not equal to zero, because vertical lines cannot be expressed in slope-intercept form due to an undefined slope. When converting back to standard form, make sure to multiply through by a common denominator if your slope or intercept contains fractions, as standard form prefers integer coefficients. Finally, double-check your signs when moving negative terms across the equals sign to prevent sign errors.