Standard Form to Slope Intercept Form Calculator – Guide & Formulas
Convert linear equations from standard form Ax + By = C to slope-intercept form y = mx + b. Find slope, y-intercept, and graph the line.
Convert any linear equation from standard form Ax + By = C to slope-intercept form y = mx + b. Instantly find the slope, y-intercept, and x-intercept.
Key Takeaway
Use the free Standard Form to Slope Intercept Form Calculator to convert linear equations from standard form ax + by = c to slope-intercept form y = mx + b. find slope, y-intercept, and graph the line. Get instant results with step-by-step explanations.
How to Use the Standard Form to Slope Intercept Form Calculator
- Enter the coefficients A, B, and C from the standard form Ax + By = C.
- Click "Convert" to see the slope-intercept form.
- Review the slope (m), y-intercept (b), and x-intercept.
- The calculator shows the step-by-step conversion process.
The Formula
Variable Definitions
- A: Coefficient of x in standard form
- B: Coefficient of y in standard form
- C: Constant term in standard form
- m: Slope = -A/B
- b: Y-intercept = C/B
Example: Convert 4x + 2y = 10 to Slope-Intercept Form
Convert the standard form equation 4x + 2y = 10 to slope-intercept form.
- Step 1: Identify coefficients: A = 4, B = 2, C = 10.
- Step 2: Subtract 4x from both sides: 2y = -4x + 10.
- Step 3: Divide by 2: y = (-4/2)x + (10/2).
- Step 4: Simplify: y = -2x + 5.
- Step 5: Slope m = -2, y-intercept b = 5, x-intercept x = 5/2 = 2.5.
Frequently Asked Questions
What is standard form?
Standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A is typically non-negative.
What is slope-intercept form?
Slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. It is the most convenient form for graphing.
How do I convert standard form to slope-intercept?
Solve for y: subtract Ax from both sides to get By = -Ax + C, then divide by B to get y = (-A/B)x + (C/B).
What if B is zero?
If B = 0, the equation becomes Ax = C, which is a vertical line. Vertical lines cannot be written in slope-intercept form because the slope is undefined.
What is the slope in standard form?
The slope is -A/B. For example, in 3x + 2y = 6, the slope is -3/2.
What is the y-intercept in standard form?
The y-intercept is C/B. For example, in 3x + 2y = 6, the y-intercept is 6/2 = 3.
What is the x-intercept?
The x-intercept is C/A (set y=0). For example, in 3x + 2y = 6, the x-intercept is 6/3 = 2.
Can I convert back from slope-intercept to standard?
Yes, rearrange y = mx + b to get -mx + y = b, then multiply to clear fractions if needed. The standard form is Ax + By = C.
Why use standard form?
Standard form is useful for finding intercepts easily, and it handles vertical lines (which slope-intercept form cannot represent).
Do I need to simplify the fractions?
It is conventional to write slope and intercept as simplified fractions or decimals. The calculator provides both forms.