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Point-Slope Formula:
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The point-slope formula is a linear equation that describes a line using a single point on the line and the slope of the line. It's particularly useful for writing the equation of a line when you know one point and the slope.
The calculator uses the point-slope formula:
Where:
Explanation: The formula calculates the y-value for any 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 writing linear equations, graphing lines, and solving problems involving linear relationships. It's particularly useful when you have a point and slope but not the y-intercept.
Tips: Enter the coordinates of your known point (x₁, y₁), the slope of the line (m), and the x-value for which you want to find the corresponding y-value. All values are unitless as this is a mathematical relationship.
Q1: How is point-slope form different from slope-intercept form?
A: Point-slope form uses a specific point and slope (y - y₁ = m(x - x₁)), while slope-intercept form uses the slope and y-intercept (y = mx + b).
Q2: Can I use this calculator if I only have two points?
A: First calculate the slope using the two points (m = (y₂ - y₁)/(x₂ - x₁)), then use one point and the slope in this calculator.
Q3: What if my slope is zero or undefined?
A: The calculator handles all slope values. A slope of zero gives a horizontal line, while an undefined slope (division by zero) would require a different approach.
Q4: Can I find x if I know y using this formula?
A: Yes, you can rearrange the formula to solve for x: x = (y - y₁)/m + x₁
Q5: Are the results always exact?
A: For integer inputs, results are exact. For decimal inputs, results are rounded to 4 decimal places for clarity.