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Point Slope Equation:
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The point slope equation is a linear equation format that describes a line using a known point on the line and the slope of the line. The general form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
The calculator uses two points to determine the point slope equation:
Where:
Explanation: The calculator first calculates the slope using the two given points, then constructs the point slope equation using the first point and the calculated slope.
Details: The point slope form is particularly useful when you know a point on the line and the slope. It's commonly used in calculus, physics problems involving linear motion, and various engineering applications where linear relationships need to be expressed.
Tips: Enter the coordinates of two distinct points. The x-coordinates must be different to avoid division by zero. All values should be real numbers.
Q1: What if my two points have the same x-coordinate?
A: If x₁ = x₂, the line is vertical and the slope is undefined. The calculator will show an error message in this case.
Q2: Can I use this for non-linear equations?
A: No, the point slope form is specifically for linear equations. It only works for straight lines.
Q3: How accurate is the calculation?
A: The calculation is mathematically exact. The result is rounded to 4 decimal places for readability.
Q4: What's the difference between point slope and slope intercept form?
A: Point slope form uses a specific point and slope, while slope intercept form (y = mx + b) uses the slope and y-intercept.
Q5: Can I convert point slope form to other linear forms?
A: Yes, point slope form can be algebraically manipulated into slope intercept form or standard form (Ax + By = C).