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Point Slope Equation:
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The point-slope form is a linear equation format that describes a line using a known point on the line and the slope of the line. It is expressed as y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope.
The calculator uses the point-slope equation:
Where:
Explanation: This form is particularly useful when you know one point on the line and the slope, allowing you to write the equation of the line quickly.
Details: The point-slope form is essential in algebra and coordinate geometry for writing linear equations when given a point and slope. It's particularly useful for finding equations of tangent lines and for linear approximation.
Tips: Enter the y-coordinate of your known point, the slope of the line, and the x-coordinate of your known point. All values should be numerical values.
Q1: When should I use point-slope form instead of slope-intercept form?
A: Use point-slope form when you know a point on the line and the slope, but not necessarily the y-intercept. It's often more convenient than slope-intercept form in these situations.
Q2: Can point-slope form be converted to other forms?
A: Yes, point-slope form can be easily converted to slope-intercept form (y = mx + b) or standard form (Ax + By = C) through algebraic manipulation.
Q3: What if my slope is zero or undefined?
A: If slope is zero, you have a horizontal line (y = y₁). If slope is undefined, you have a vertical line (x = x₁). The calculator handles these cases correctly.
Q4: Can I use decimal or fractional values?
A: Yes, the calculator accepts both decimal and whole number inputs for all parameters.
Q5: How accurate is the point-slope equation?
A: The point-slope form is mathematically exact for linear equations. The accuracy depends on the precision of your input values.