Slope Intercept Form Calculator – Guide & Formulas
Convert any linear equation to slope-intercept form y = mx + b. Identify slope, y-intercept, x-intercept, and graph the line.
Convert any linear equation to slope-intercept form y = mx + b. Enter standard form, two points, or point-slope form to find the slope, y-intercept, and graph.
Key Takeaway
Use the free Slope Intercept Form Calculator to convert any linear equation to slope-intercept form y = mx + b. identify slope, y-intercept, x-intercept, and graph the line. Get instant results with step-by-step explanations.
How to Use the Slope Intercept Form Calculator
- Select the input format: Standard form, Two points, or Point-slope form.
- Enter the values for your chosen format.
- Click "Calculate" to convert to slope-intercept form.
- Review the slope (m), y-intercept (b), x-intercept, and graph.
The Formula
Variable Definitions
- m: Slope of the line (rise/run)
- b: Y-intercept (where line crosses the y-axis)
- x: Independent variable
- y: Dependent variable
- x-intercept: Where the line crosses the x-axis: x = -b/m
Example: Convert 3x + 2y = 12 to Slope-Intercept Form
Convert the standard form equation 3x + 2y = 12 to slope-intercept form.
- Step 1: Start with 3x + 2y = 12.
- Step 2: Subtract 3x from both sides: 2y = -3x + 12.
- Step 3: Divide by 2: y = (-3/2)x + 6.
- Step 4: Slope m = -3/2 = -1.5, y-intercept b = 6.
- Step 5: x-intercept: 0 = -1.5x + 6, so x = 4. The x-intercept is (4, 0).
Frequently Asked Questions
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 one of the most common ways to write a linear equation.
How do I find the slope from slope-intercept form?
The slope (m) is the coefficient of x. In y = 3x + 2, the slope is 3.
How do I find the y-intercept?
The y-intercept (b) is the constant term. In y = 3x + 2, the y-intercept is 2, which is the point (0, 2).
How do I find the x-intercept?
Set y = 0 and solve for x: 0 = mx + b, so x = -b/m. The x-intercept is (-b/m, 0).
How do I convert from standard form to slope-intercept?
Solve for y: Ax + By = C becomes y = (-A/B)x + (C/B). The slope is -A/B and the y-intercept is C/B.
What does a positive slope look like?
A positive slope means the line rises from left to right. A slope of 2 means y increases by 2 for every 1-unit increase in x.
What does a zero slope mean?
A zero slope (m = 0) means the line is horizontal. The equation becomes y = b, a constant value.
What is an undefined slope?
An undefined slope occurs for vertical lines where the run is zero. The equation becomes x = a, a constant x value.
How do I graph a line in slope-intercept form?
Plot the y-intercept (0, b) first, then use the slope (rise/run) to find a second point. Draw a line through both points.
Can I use this for non-linear equations?
No, slope-intercept form only applies to linear equations (straight lines). For curves, you need other forms like quadratic or exponential equations.