Preset examples
Formula used
The slope-intercept formula is y = mx + b. The letter m represents the line slope. The letter b marks the vertical intercept point.
- Calculate y: y = mx + b
- Calculate m: m = (y - b) / x
- Calculate x: x = (y - b) / m
- Calculate b: b = y - mx
- Two-point slope: m = (y₂ - y₁) / (x₂ - x₁)
- X-intercept: x = -b / m
- Perpendicular slope: -1 / m
How to use this calculator
Choose the calculation mode matching your problem. Enter all required numbers or fractions carefully. Select Calculate to view steps, forms, and graphs.
Adjust precision for rounded decimal results. Choose fraction mode for exact-looking rational answers. Change table limits before calculating another useful coordinate set.
Worked example
Consider the equation y = 2x + 3. Substitute x = 4 into the equation. The result is y = 11 after simplification.
| Step | Operation | Result |
|---|---|---|
| 1 | Write the formula | y = mx + b |
| 2 | Substitute values | y = 2(4) + 3 |
| 3 | Multiply | y = 8 + 3 |
| 4 | Add | y = 11 |
Frequently asked questions
What does y = mx + b represent?
It represents a straight line equation. The slope controls vertical change per horizontal unit. The intercept shows where the line crosses y.
What does the slope m mean?
Slope measures the line's rise over run. Positive slopes rise from left to right. Negative slopes fall from left to right.
What does the y-intercept b mean?
The y-intercept is the value when x equals zero. Its coordinate is always written as (0, b). It locates the line's y-axis crossing point.
Can the calculator accept fractions?
Yes, it accepts simple and mixed fractions. Enter values like 3/4 or 2 1/3. Fraction mode also displays decimal equivalents for clarity.
How is an x-intercept calculated?
Set y equal to zero first. Then solve 0 = mx + b. The intercept becomes x = -b divided by m.
What happens when the slope equals zero?
A zero slope creates a horizontal line. Its y-value remains constant for every x. A perpendicular line then becomes vertical.
Why can vertical lines not use this form?
Vertical lines have an undefined slope. Their x-value stays constant while y changes. They use equations like x = 4.
How are parallel and perpendicular slopes related?
Parallel lines have identical slopes. Perpendicular slopes are negative reciprocals of each other. Their product equals negative one when defined.
How does point checking work?
The calculator substitutes the point's x-coordinate. It compares the resulting y with entered y. Matching values confirm the point lies on the line.