1. What is Point Slope Form?

The point slope form is a linear equation format that uses a known point on the line (x₁, y₁) and the slope (m) of the line. It's expressed as: y - y₁ = m(x - x₁). This form is particularly useful when you have one point and the slope of the line.

2. How to Calculate X-Intercept?

To find the x-intercept from point slope form, set y = 0 and solve for x:

Where:

• \( y_1 \) — Y-coordinate of the known point
• \( m \) — Slope of the line
• \( x_1 \) — X-coordinate of the known point
• \( x_{int} \) — X-intercept value

3. Applications of Point Slope Form

Details: Point slope form is widely used in coordinate geometry, physics problems involving linear motion, economics for demand/supply curves, and engineering calculations requiring linear approximations.

4. Using the Calculator

Tips: Enter the y-coordinate of your point, the slope of the line, and the x-coordinate of your point. The slope cannot be zero. All values can be positive, negative, or decimal numbers.

5. Frequently Asked Questions (FAQ)

Q1: What if the slope is zero?
A: If the slope is zero, the line is horizontal and may not have an x-intercept (if y₁ ≠ 0) or has infinitely many x-intercepts (if y₁ = 0).

Q2: Can I use this for vertical lines?
A: No, vertical lines have undefined slope and cannot be expressed in point slope form. They have the equation x = constant.

Q3: What's the difference between x-intercept and y-intercept?
A: X-intercept is where the line crosses the x-axis (y=0), while y-intercept is where it crosses the y-axis (x=0).

Q4: How accurate are the calculations?
A: The calculator provides results with 4 decimal places precision, suitable for most mathematical applications.

Q5: Can I use this for non-linear equations?
A: No, point slope form is specifically for linear equations. Non-linear equations require different forms and methods.