Руководство по калькулятору наклона прямой

What This Calculator Does

This slope calculator analyzes the line passing through two points in a coordinate plane. It returns rise, run, slope, y-intercept when available, the point-to-point distance, and a readable line equation.

When to Use It

• You want the slope between two points.
• You need to check whether a line is increasing, decreasing, or vertical.
• You want the line equation in a quick numeric form.
• You need both slope and point-to-point distance in one place.

Inputs Explained

Enter two different points:

• first point: x1, y1
• second point: x2, y2

These values define one line in 2D space.

How the Calculation Works

The page computes:

• rise = y2 - y1
• run = x2 - x1
• slope = rise / run when run is not zero
• distance = sqrt(run² + rise²)

If the line is not vertical, the page also calculates the y-intercept and writes the line in slope-intercept form. If run = 0, the line is vertical and the result becomes x = constant.

Example

For points (1, 2) and (4, 8):

• rise = 6
• run = 3
• slope = 2

The line is not vertical, so the page also derives the intercept and equation.

How to Understand the Result

• positive slope means the line rises from left to right
• negative slope means the line falls from left to right
• zero slope means a horizontal line
• undefined slope means a vertical line

Common Mistakes

• Entering the same point twice.
• Expecting a y-intercept for a vertical line.
• Mixing up rise and run order after entering points.

FAQ

Why is the slope undefined sometimes?

That happens when x1 = x2, so the run is zero and division by zero is not defined.

Is the displayed distance the same as horizontal or vertical difference?

No. It is the Euclidean distance, not just dx or dy.

Does point order matter?

It changes the sign of rise and run together, but the final slope remains the same.

Notes

This tool is useful for coordinate geometry, graphing practice, and quick line analysis. For midpoint-specific work, use the distance and midpoint calculator alongside it.