Slope Calculator With 2 Points And Angle Formula

Slope Formulas:

\[ \text{Slope} = \tan(\theta \times \pi / 180) \] \[ \text{Slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Angle (degrees):

Point 1 X-coordinate:

Point 1 Y-coordinate:

Point 2 X-coordinate:

Point 2 Y-coordinate:

Calculated Slope:

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1. What is Slope?

Slope measures the steepness or incline of a line, representing the ratio of vertical change to horizontal change between two points on the line.

2. How Does the Calculator Work?

The calculator uses two formulas to determine slope:

\[ \text{From Angle: Slope} = \tan(\theta \times \pi / 180) \] \[ \text{From Points: Slope} = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

\( \theta \) — Angle in degrees
\( (x_1, y_1) \) — Coordinates of first point
\( (x_2, y_2) \) — Coordinates of second point

Explanation: The angle formula converts degrees to radians and applies the tangent function. The points formula calculates the ratio of vertical to horizontal change.

3. Importance of Slope Calculation

Details: Slope is fundamental in mathematics, physics, engineering, and many real-world applications like road construction, roof pitch, and graph analysis.

4. Using the Calculator

Tips: Enter either the angle (degrees) OR two points' coordinates. The calculator will compute the slope using the appropriate formula.

5. Frequently Asked Questions (FAQ)

Q1: What does a slope of 0 mean?
A: A slope of 0 indicates a perfectly horizontal line (no vertical change).

Q2: What does an undefined slope mean?
A: Undefined slope occurs with vertical lines when x-coordinates are equal (division by zero).

Q3: How does slope relate to angle?
A: The angle is the arctangent of the slope. A 45° angle has slope = 1.

Q4: Can slope be negative?
A: Yes, negative slope indicates the line is decreasing (falling from left to right).

Q5: What's the maximum possible slope?
A: There's no maximum - as the angle approaches 90°, the slope approaches infinity.