y Intercept Calculator

Linear equations are commonly expressed in standard form as Ax + By = C. To find the y-intercept, where the line crosses the vertical y-axis, we set x to zero, which simplifies the formula to y = -C / B. Similarly, the x-intercept occurs where y is zero, calculated as x = -C / A. The slope (m) of the line is determined by the ratio -A / B. When working with absolute values, the calculator automatically converts negative coordinate outputs into their positive distance magnitudes.

Let us find the key parameters for the linear equation 2x + 3y = 6. Here, A = 2, B = 3, and C = 6. First, compute the slope using m = -A / B, which gives m = -2/3 or approximately -0.667. Next, calculate the y-intercept using y_int = -C / B, resulting in -6 / 3 = -2. This means the line crosses the y-axis at the coordinate (0, -2). Finally, find the x-intercept using x_int = -C / A, which equals -6 / 2 = -3, placing the x-intercept at (-3, 0).

Always double-check that your linear equation is correctly organized before inputting values for A, B, and C. Watch out for signs; a misplaced negative sign can completely invert your slope and intercept values. If your equation has a B value of zero, it represents a vertical line, meaning it has no y-intercept and an undefined slope.