What This Calculator Does
This tool converts a linear equation written in standard form, Ax + By = C, into the more familiar slope-intercept form, y = mx + b. By entering the three coefficients A, B, and C, you instantly get the slope (m) and the y-intercept (b), making it easy to graph the line or compare equations.
How to Use It
Enter the coefficient of x as A, the coefficient of y as B, and the constant on the right side as C. The calculator solves for y and returns the slope and intercept. If B = 0, the line is vertical (\(x = C/A\)) and has no slope-intercept form.
The Formula Explained
Starting from \(Ax + By = C\), subtract Ax from both sides to get \(By = -Ax + C\), then divide every term by B: $$y = -\frac{A}{B}\,x + \frac{C}{B}$$ Comparing with \(y = mx + b\) gives the slope \(m = -\frac{A}{B}\) and the y-intercept \(b = \frac{C}{B}\).
Worked Example
Take \(2x + 4y = 8\). Here \(A = 2\), \(B = 4\), \(C = 8\). The slope is $$m = -\frac{2}{4} = -0.5$$ and the y-intercept is $$b = \frac{8}{4} = 2$$ So the equation in slope-intercept form is $$y = -0.5x + 2$$
FAQ
What if B is zero? Then the equation describes a vertical line \(x = C/A\), which cannot be written as \(y = mx + b\) because its slope is undefined.
Can A be zero? Yes. If \(A = 0\) the slope is 0 and the line is horizontal at \(y = C/B\).
Does sign matter? Yes — the negative sign in \(m = -\frac{A}{B}\) is essential. Forgetting it is the most common mistake when converting forms.
