Slope Calculator
Slope is rise over run, and the fraction is where the understanding lives: from (2, 3) to (7, 8) the line rises 5 over a run of 5 - slope 1, a 45° line, clean and exact. Enter any two points and this calculator returns the slope as both decimal and reduced fraction, the inclination angle in degrees, the y-intercept, and the slope any perpendicular line would need - the four numbers algebra homework and roof-pitch questions actually ask for.
The worked note shows the rise-over-run division with your numbers substituted, so the answer demonstrates its own method. Vertical lines are handled as the special case they are - undefined slope, 90°, no intercept - rather than crashing into a division by zero. Points are remembered between visits for multi-part problems, and the page sits with the fraction and degrees-radians tools in the study corner.
How to use
- Enter the x and y of both points.
- Read the slope as decimal and fraction, plus angle and y-intercept.
- Use the perpendicular slope in the note for parallel/perpendicular questions.
Frequently asked questions
What is the slope formula?
m = (y₂ - y₁) / (x₂ - x₁) - the vertical change between the points divided by the horizontal change. From (2, 3) to (7, 8): (8-3)/(7-2) = 5/5 = 1. The note line reproduces exactly this substitution with your values.
What does a negative slope mean?
The line falls as it moves left to right - downhill in standard reading order. Positive slopes rise, zero slopes run horizontally (both y values equal), and undefined slopes are vertical (both x values equal). The direction is named in the result note.
How do I find the y-intercept from two points?
Solve y = mx + b with one of your points: b = y₁ - m·x₁. The calculator does this and hands you the full line equation, which is usually the second half of the same homework problem.
How are slope and angle related?
The inclination angle is the arctangent of the slope: slope 1 is 45°, slope √3 ≈ 1.732 is 60°, and roofers flip the relationship - a 6:12 pitch means slope 0.5, about 26.57°. The angle stat connects the algebra view with the physical one.