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Point-Slope Form Equation:
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The point-slope form is a linear equation format used to describe a line using a known point on the line and its slope. It's particularly useful for writing equations when you know one point and the slope of the line.
The calculator uses the point-slope form equation:
Where:
Explanation: This form directly expresses the relationship between any point (x, y) on the line and a specific known point (x₁, y₁) using the slope m.
Details: The point-slope form is essential in algebra and coordinate geometry for quickly writing linear equations when given a point and slope. It's particularly useful for finding tangent lines and for linear approximation in calculus.
Tips: Enter the y-coordinate of your known point, the slope of the line, and the x-coordinate of your known point. The calculator will generate the complete point-slope form equation.
Q1: How is point-slope form different from 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. Both can represent the same line.
Q2: Can I convert point-slope form to slope-intercept form?
A: Yes, by solving for y: y = m(x - x₁) + y₁, which simplifies to y = mx + (y₁ - mx₁).
Q3: When is point-slope form most useful?
A: When you have a specific point and the slope, but don't know the y-intercept, point-slope form is the most efficient way to write the equation.
Q4: What if my slope is zero or undefined?
A: For zero slope (horizontal line), the equation becomes y = y₁. For undefined slope (vertical line), it becomes x = x₁.
Q5: Can I use decimal values for the coordinates and slope?
A: Yes, the calculator accepts decimal values for all inputs, providing precise equation results.