Equation Calculator Given Slope and Point

Point-Slope Equation:

\[ y - y_1 = m(x - x_1) \]

Slope (m):

unitless

X-coordinate of Point (x₁):

unitless

Y-coordinate of Point (y₁):

unitless

Point-Slope Equation:

Slope-Intercept Form:

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1. What is the Point-Slope Equation?

The point-slope form is a linear equation format that uses a known point on the line (x₁, y₁) and the slope (m) to define the line. It's particularly useful when you have a point and the slope but need to find other points on the line.

2. How Does the Calculator Work?

The calculator uses the point-slope equation:

\[ y - y_1 = m(x - x_1) \]

Where:

\( y \) — Dependent variable (unitless)
\( y_1 \) — Y-coordinate of known point (unitless)
\( m \) — Slope of the line (unitless)
\( x \) — Independent variable (unitless)
\( x_1 \) — X-coordinate of known point (unitless)

Explanation: The equation shows the relationship between any point (x, y) on the line and the known point (x₁, y₁), with the slope m determining the steepness and direction of the line.

3. Importance of Point-Slope Form

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, physics, and engineering applications where instantaneous rates of change are known.

4. Using the Calculator

Tips: Enter the slope value (m), and the coordinates of the known point (x₁, y₁). The calculator will provide both the point-slope form and the converted slope-intercept form of the equation.

5. Frequently Asked Questions (FAQ)

Q1: When should I use point-slope form vs slope-intercept form?
A: Use point-slope form when you have a point and slope. Use slope-intercept form (y = mx + b) when you have the slope and y-intercept.

Q2: Can I use this for vertical lines?
A: No, vertical lines have undefined slope and require the equation x = constant.

Q3: What if my slope is zero?
A: A zero slope indicates a horizontal line, which simplifies to y = y₁.

Q4: How do I convert to standard form (Ax + By = C)?
A: Expand and rearrange the equation: multiply through and move all terms to one side.

Q5: Can I find multiple points on the line?
A: Yes, once you have the equation, you can substitute any x-value to find the corresponding y-value.