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Point-Slope Formula:
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The point-slope formula is a linear equation that describes a line using its slope and one point on the line. It provides a straightforward way to find the equation of a line or calculate other points on the same line.
The calculator uses the point-slope formula:
Where:
Explanation: The formula calculates the y-value for a given x-value based on a known point (x₁, y₁) and the slope m of the line.
Details: The point-slope form is essential in algebra and coordinate geometry for finding linear equations, graphing lines, and solving various mathematical problems involving linear relationships.
Tips: Enter the coordinates of the known point (x₁, y₁), the slope (m), and the x-value for which you want to find the corresponding y-value. All values are unitless.
Q1: What is the difference between point-slope and slope-intercept form?
A: Point-slope form uses one point and the slope, while slope-intercept form uses the slope and y-intercept. Both can represent the same line.
Q2: Can I use this formula for vertical lines?
A: No, vertical lines have undefined slope and cannot be represented using the point-slope form.
Q3: What if I have two points instead of a point and slope?
A: You can calculate the slope first using m = (y₂ - y₁)/(x₂ - x₁), then use the point-slope formula with either point.
Q4: Are there limitations to this formula?
A: The formula only works for linear relationships and requires that the line is not vertical (infinite slope).
Q5: Can this be used for real-world applications?
A: Yes, the point-slope form is widely used in physics, engineering, economics, and other fields to model linear relationships between variables.