Standard form is convenient for intercepts and integer coefficients; slope-intercept form is convenient for graphing. Converting between them is routine algebra.
How to use the Standard Form to Slope Intercept Form Calculator
- Calculation mode
- A
- B
- C
- m
- b
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How it works
From standard form, solve for y: m = −A/B and b = C/B. From slope-intercept form, move the x term: −mx + y = b, then scale to integers.
Formula
Ax + By = C ⇔ y = −(A/B)x + C/B
Worked example
Inputs — Calculation mode: Standard → slope-intercept; A: 2; B: 3; C: 6.
Results — Result = y = (−2/3)x + 2; Original line = 2x + 3y = 6; Slope = −2/3; y-intercept = 2; x-intercept = 3.
Key terms
- Standard form
- Ax + By = C.
Frequently asked questions
How do I convert 2x + 3y = 6?
3y = −2x + 6, so y = −(2/3)x + 2.
What if B = 0?
The line is vertical, x = C/A, with no slope-intercept form.
Why use integer coefficients?
Standard form conventionally has integers with A ≥ 0.
What are the intercepts of Ax + By = C?
x = C/A and y = C/B.