What is the Solve for y Calculator?
This calculator rearranges a linear equation written in standard form, \(Ax + By = C\), so that y is by itself on one side. Given the coefficients A, B and C plus a chosen x value, it instantly returns the matching value of y. It also reports the slope and y-intercept so you can see the equation in slope-intercept form, \(y = mx + b\).
How to use it
Enter the coefficient of x (A), the coefficient of y (B), the constant (C), and the x value you want to evaluate. Press calculate and the tool isolates y using $$y = \frac{C - Ax}{B}$$ If B is zero the equation has no unique y and the result is left at zero, since you cannot divide by zero.
The formula explained
Starting from \(Ax + By = C\), subtract Ax from both sides to get \(By = C - Ax\). Then divide both sides by B to isolate y: $$y = \frac{C - Ax}{B}$$ Writing this as \(y = \left(-\frac{A}{B}\right)x + \frac{C}{B}\) reveals the slope \(m = -\frac{A}{B}\) and the y-intercept \(b = \frac{C}{B}\), which are useful for graphing the line.
Worked example
Suppose \(2x + 3y = 12\) and you want y when \(x = 3\). Substitute: $$y = \frac{12 - 2\cdot 3}{3} = \frac{12 - 6}{3} = \frac{6}{3} = 2$$ So \(y = 2\). The slope is \(-\frac{A}{B} = -\frac{2}{3} \approx -0.6667\) and the y-intercept is \(\frac{C}{B} = \frac{12}{3} = 4\).
FAQ
What if B is 0? Then the term By disappears and y cannot be solved uniquely — the equation only constrains x. The calculator returns 0 in that case.
Can A or C be negative? Yes. Enter negative values normally; the algebra works for any real coefficients.
Does this only work for one x? The y value is specific to the x you enter, but the reported slope and intercept describe the whole line.
