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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 directly.
Details: The point-slope form is essential in algebra and coordinate geometry for quickly writing the equation of a line when given a point and slope. It's particularly useful in calculus and physics applications where instantaneous rates of change are known.
Tips: Enter the y-coordinate of the known point, the slope of the line, and the x-coordinate of the known point. All values should be entered as real numbers.
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 more direct than converting through other forms.
Q2: Can point-slope form represent vertical lines?
A: No, point-slope form cannot represent vertical lines because vertical lines have undefined slope. Vertical lines must be represented as x = constant.
Q3: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope through the parentheses and then solve for y: y = m(x - x₁) + y₁ = mx - mx₁ + y₁.
Q4: What if my slope is zero?
A: If the slope is zero, you have a horizontal line. The equation simplifies to y = y₁, where y₁ is the y-coordinate of your known point.
Q5: Can I use this form for non-linear equations?
A: No, the point-slope form is specifically for linear equations. For non-linear equations, different forms and methods are required.