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Point-Slope Form Equation:
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The point-slope form is a way to express the equation of a straight line. It is particularly useful when you know the slope of the line and one point on the line. The general form is 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 form equation:
Where:
Explanation: The equation calculates the y-value for any given x-value based on a known point and the slope of the line.
Details: The point-slope form is essential in algebra and coordinate geometry as it provides a straightforward method to write the equation of a line when you know its slope and a point it passes through. It's particularly useful for writing equations quickly without needing to convert to other forms.
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 coordinates and ratios.
Q1: What's the difference between point-slope form and slope-intercept form?
A: Point-slope form (y - y₁ = m(x - x₁)) requires a point and slope, while slope-intercept form (y = mx + b) requires the slope and y-intercept.
Q2: Can I use this form for vertical lines?
A: No, vertical lines have undefined slope and cannot be represented in point-slope form. They are represented as x = constant.
Q3: How do I convert point-slope form to slope-intercept form?
A: Distribute the slope and then isolate y: y = m(x - x₁) + y₁ = mx - mx₁ + y₁.
Q4: What if I have two points but no slope?
A: First calculate the slope using m = (y₂ - y₁)/(x₂ - x₁), then use either point in the point-slope form.
Q5: Are there limitations to this form?
A: The main limitation is that it requires knowing both a point and the slope. It's also not as convenient as slope-intercept form for graphing.