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Point-Slope Form Equation:
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The point-slope form is a linear equation format that defines a line using its slope and a single point on the line. It's particularly useful when you know one point on the line and the slope.
The calculator uses the point-slope form equation:
Where:
Explanation: This form directly relates the difference in y-values to the difference in x-values through the slope, making it ideal for calculating unknown y-values given x-values.
Details: The point-slope form is essential in algebra and coordinate geometry for writing linear equations when a point and slope are known. It's particularly useful for finding equations of tangent lines and for linear interpolation.
Tips: Enter the coordinates of the known point (x₁, y₁), the slope of the line (m), and the x-value for which you want to calculate the corresponding y-value. All values are unitless as they represent coordinate positions.
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 this 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 accurate are the calculations?
A: The calculator provides results with 4 decimal places precision, which is sufficient for most mathematical and engineering applications.
Q4: Can I use this for non-linear equations?
A: No, this calculator is specifically designed for linear equations. The point-slope form only applies to straight lines.
Q5: What if I need to find the equation of the line instead of a specific point?
A: The point-slope form itself IS the equation of the line. You can rearrange it to slope-intercept form (y = mx + b) if needed.