1. What is Point Slope Form?

The point-slope form is a linear equation format that expresses the relationship between two variables using a known point on the line and the slope of the line. It is particularly useful for writing the equation of a line when you know one point and the slope.

2. How Does the Calculator Work?

The calculator uses the point-slope formula:

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: This form allows you to find the y-value for any given x-value when you know the slope of the line and one point that lies on it.

3. Applications of Point Slope Form

Details: Point-slope form is widely used in algebra, geometry, physics, and engineering for linear modeling, predicting values, and analyzing relationships between variables.

4. Using the Calculator

Tips: Enter the slope value, coordinates of the known point (x₁, y₁), and the x-value for which you want to find the corresponding y-value. All values should be numerical.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between point-slope form and slope-intercept form?
A: Point-slope form uses a specific point and slope, while slope-intercept form (y = mx + b) uses the slope and y-intercept.

Q2: Can I use this form for vertical lines?
A: No, point-slope form cannot represent vertical lines because vertical lines have undefined slope.

Q3: How do I convert point-slope form to standard form?
A: Rearrange the equation to get all terms on one side: Ax + By = C.

Q4: What if I have two points instead of a point and 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 point-slope form?
A: It's specifically designed for linear relationships and cannot represent non-linear functions.