Slope Intercept Calculator from 2 Points

Slope-Intercept Formula:

\[ y = mx + b \]

Where: \( m = \frac{y_2 - y_1}{x_2 - x_1} \), \( b = y_1 - m x_1 \)

x₁ (x-coordinate of first point):

unitless

y₁ (y-coordinate of first point):

unitless

x₂ (x-coordinate of second point):

unitless

y₂ (y-coordinate of second point):

unitless

Slope-Intercept Equation:

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1. What is the Slope-Intercept Form?

The slope-intercept form is a linear equation of the form y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is widely used in algebra and coordinate geometry to describe straight lines.

2. How Does the Calculator Work?

The calculator uses the following formulas:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \] \[ b = y_1 - m x_1 \] \[ y = mx + b \]

Where:

\( m \) — Slope of the line (unitless)
\( b \) — Y-intercept (unitless)
\( x_1, y_1 \) — Coordinates of the first point
\( x_2, y_2 \) — Coordinates of the second point

Explanation: The calculator first calculates the slope using the two given points, then uses one point and the slope to find the y-intercept, finally constructing the slope-intercept equation.

3. Importance of Slope-Intercept Form

Details: The slope-intercept form is fundamental in mathematics for graphing linear equations, analyzing rates of change, and solving real-world problems involving linear relationships. It provides immediate information about the line's steepness and where it crosses the y-axis.

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The x-coordinates must be different to avoid division by zero. The calculator will provide the slope-intercept equation of the line passing through these two points.

5. Frequently Asked Questions (FAQ)

Q1: What if my points have the same x-coordinate?
A: If x₁ = x₂, the line is vertical and cannot be expressed in slope-intercept form (infinite slope).

Q2: How accurate are the results?
A: The calculator provides results with 4 decimal places precision, suitable for most mathematical applications.

Q3: Can I use this for negative slopes?
A: Yes, the calculator handles both positive and negative slopes correctly.

Q4: What if the line passes through the origin?
A: If the line passes through (0,0), the y-intercept (b) will be 0.

Q5: Can I use this for fractional coordinates?
A: Yes, the calculator accepts decimal values for all coordinates.