Standard Form to Slope-Intercept Form Calculator
Enter coefficients A, B and constant C from the standard form Ax + By = C to get the slope-intercept equation y = mx + b, slope, intercepts and a line plot.
Start with standard form
Isolate y: subtract Ax
Divide both sides by B
Simplify coefficients
- 1
Slope m = −A ÷ B
−3 ÷ 2 = -1.5000 - 2
y-intercept b = C ÷ B
6 ÷ 2 = 3 - 3
Angle of inclination
arctan(-1.5) = -56.31°Angle the line makes with the positive x-axis.
How does this calculator work?
Convert Ax + By = C → y = mx + b by isolating y: slope m = −A/B, y-intercept b = C/B, x-intercept = C/A. Example: 3x + 2y = 6 → y = −(3/2)x + 3 (slope −1.5, y-int 3, x-int 2). If B = 0 the line is vertical and has no slope-intercept form.
Formula
How this is calculated
Standard form Ax + By = C is often encountered in algebra textbooks and systems-of-equations problems because it treats x and y symmetrically and uses integer coefficients. Slope-intercept form y = mx + b is preferred for graphing because it directly reveals the slope m and the y-intercept b.
To convert, isolate y on the left: subtract Ax from both sides to get By = −Ax + C, then divide through by B to get y = (−A/B)x + (C/B). The slope is therefore m = −A/B and the y-intercept is b = C/B. If B = 0 the equation becomes Ax = C, describing a vertical line x = C/A which has no slope and no slope-intercept form.
The x-intercept (where the line crosses the x-axis) is found by setting y = 0 in the original equation: Ax = C, so x = C/A (undefined when A = 0, meaning a horizontal line never crosses the x-axis unless C = 0). The angle of inclination θ = arctan(m) gives the angle the line makes with the positive x-axis.
Frequently asked questions
Standard form is Ax + By = C, where A, B and C are typically integers and A is non-negative. It is equivalent to any other linear form (slope-intercept, point-slope) — the same line just written differently.
If B = 0 the equation Ax = C describes a vertical line passing through x = C/A. There is no y-term, so there is no y-intercept and the slope is undefined. The slope-intercept form does not apply.
Start with y = mx + b; subtract y from both sides and multiply through to clear fractions: −mx + y = b. Rearranged with A = −m and B = 1: −mx + y = b. Multiply by −1 if you want A positive: mx − y = −b.
Also known as
TG we-Calculate Editorial Team. (2026). Standard Form to Slope-Intercept Form Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/standard-form-to-slope-intercept-form-calculator
TG we-Calculate Editorial Team. "Standard Form to Slope-Intercept Form Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/standard-form-to-slope-intercept-form-calculator.
TG we-Calculate Editorial Team, "Standard Form to Slope-Intercept Form Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/standard-form-to-slope-intercept-form-calculator
@misc{wecalculate_standard_form_to_slope_intercept_form_calculator, title = {Standard Form to Slope-Intercept Form Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/standard-form-to-slope-intercept-form-calculator}}, year = {2026}, note = {TG we-Calculate} }
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