Calculator Input
Formula Used
The slope between two points is the ratio of vertical change to horizontal change.
m = (y₂ - y₁) / (x₂ - x₁)
rise = y₂ - y₁
run = x₂ - x₁
angle = arctan(m)
grade = m × 100%
If x₂ - x₁ = 0, the line is vertical. Its slope is undefined.
How to Use This Calculator
- Enter the first point as
x₁andy₁. - Enter the second point as
x₂andy₂. - You may use whole numbers, decimals, fractions, or mixed numbers.
- Choose the decimal precision for rounded outputs.
- Press the calculate button.
- Review the simplified fraction, decimal slope, angle, grade, and equation.
- Use the CSV or PDF buttons to save your result.
Example Data Table
| x₁ | y₁ | x₂ | y₂ | Rise | Run | Slope | Line Type |
|---|---|---|---|---|---|---|---|
| 1/2 | 3/4 | 5/2 | 11/4 | 2 | 2 | 1 | Rising |
| -2 | 4 | 6 | 0 | -4 | 8 | -1/2 | Falling |
| 3 | 7/2 | 9 | 7/2 | 0 | 6 | 0 | Horizontal |
| 5 | 1 | 5 | 8 | 7 | 0 | Undefined | Vertical |
Understanding Fraction Slopes
What the Slope Shows
A slope describes how fast a line rises or falls. It compares vertical change with horizontal change. In coordinate geometry, this change is measured between two points. The top part is called rise. The bottom part is called run. A fraction slope keeps this relationship exact.
Why Fractions Are Useful
Decimal slopes are easy to read. Fraction slopes are usually more exact. For example, 0.333333 is only an estimate, while 1/3 is exact. This calculator reduces every fraction. It also accepts mixed numbers, decimals, and negative values. That makes it useful for algebra, graphing, and analytic geometry.
Positive, Negative, and Zero Slopes
A positive slope rises from left to right. A negative slope falls from left to right. A zero slope is horizontal. It happens when both y-values are equal. A vertical line has no defined slope. It happens when both x-values are equal. The calculator identifies each case and shows a clear message.
Line Forms and Graphing
The tool also builds useful line forms. Slope-intercept form helps you see the y-intercept. Point-slope form helps when one point and the slope are known. The graph gives a visual check. The two entered points are plotted, and the connecting line is drawn. This helps students confirm direction, steepness, and position quickly.
Study and Export Benefits
The result section includes rise, run, slope fraction, decimal slope, grade, angle, equation, and segment length. You can download results as CSV for spreadsheets. You can also download a PDF for assignments, notes, or quick review. Use exact fraction input when possible for the cleanest answer.
FAQs
1. What is a slope fraction?
A slope fraction is rise divided by run. It shows vertical change over horizontal change between two points.
2. Can I enter mixed numbers?
Yes. You can enter values like 2 1/3, -4 1/2, fractions, decimals, or whole numbers.
3. What happens if the run is zero?
The line is vertical. The calculator reports the slope as undefined because division by zero is impossible.
4. What does a negative slope mean?
A negative slope means the line falls from left to right. The y-value decreases as x increases.
5. Why is the fraction simplified?
Simplifying gives the cleanest exact ratio. It makes the slope easier to compare, graph, and use.
6. Is decimal slope also shown?
Yes. The calculator shows both exact fraction slope and rounded decimal slope using your chosen precision.
7. What is percent grade?
Percent grade is slope multiplied by 100. It is often used for ramps, roads, and incline comparisons.
8. Can I save the results?
Yes. Use the CSV download for spreadsheet data or the PDF download for a formatted report.