1. What is the Point Slope Form?

The point-slope form is a linear equation format that represents a straight line using a known point on the line (x₁, y₁) and the slope (m) of the line. It is expressed as y - y₁ = m(x - x₁).

2. How Does the Calculator Work?

The calculator uses the point-slope form equation:

Where:

• \( y \) — Dependent variable (unitless)
• \( y₁ \) — Y-coordinate of known point (unitless)
• \( m \) — Slope of the line (unitless)
• \( x \) — Independent variable (unitless)
• \( x₁ \) — X-coordinate of known point (unitless)

Explanation: The equation calculates the y-value for a given x-value based on a known point and the slope of the line.

3. Importance of Point Slope Form

Details: The point-slope form is particularly useful when you know a point on the line and the slope, making it easier to write the equation of the line without needing the y-intercept.

4. Using the Calculator

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.

5. Frequently Asked Questions (FAQ)

Q1: When should I use point-slope form?
A: Use point-slope form when you know a point on the line and the slope, but don't necessarily know the y-intercept.

Q2: How is point-slope form different from slope-intercept form?
A: Slope-intercept form (y = mx + b) requires knowing the y-intercept, while point-slope form uses any point on the line.

Q3: Can I convert point-slope form to slope-intercept form?
A: Yes, by solving for y: y = m(x - x₁) + y₁, which simplifies to y = mx - mx₁ + y₁.

Q4: 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 either point with the point-slope form.

Q5: Are there any limitations to point-slope form?
A: The form cannot represent vertical lines, as they have undefined slope.