Use the Point Slope Formula Calculator

Point Slope Formula:

\[ y - y₁ = m(x - x₁) \]

Y-coordinate of Point (y₁):

unitless

Slope (m):

unitless

X-coordinate of Point (x₁):

unitless

Point Slope Form:

Slope Intercept Form:

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1. What is the Point Slope Formula?

The point slope formula is used to find the equation of a straight line when you know the slope of the line and one point on the line. The formula is expressed as: y - y₁ = m(x - x₁), where (x₁, y₁) is the known point and m is the slope of the line.

2. How Does the Calculator Work?

The calculator uses the point slope formula:

\[ y - y₁ = m(x - x₁) \]

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 formula calculates the linear equation that passes through the given point with the specified slope. It can be rearranged to slope-intercept form (y = mx + b) for easier interpretation.

3. Importance of Point Slope Form

Details: The point slope form is particularly useful when you have a point and the slope but not the y-intercept. It's commonly used in coordinate geometry, physics problems, and various engineering applications where linear relationships need to be expressed.

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 calculator will provide both the point slope form and slope intercept form of the equation.

5. Frequently Asked Questions (FAQ)

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

Q2: Can I use this formula for vertical lines?
A: No, vertical lines have undefined slope and cannot be represented using the point slope formula. Vertical lines are represented as x = constant.

Q3: What if my slope is zero?
A: If the slope is zero, you have a horizontal line. The equation will be y = y₁ (the y-value of your point).

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for the given inputs, as it's based on algebraic principles with no approximations involved.

Q5: Can I use this for non-linear equations?
A: No, the point slope formula only applies to linear equations (straight lines). For non-linear equations, different formulas and methods are required.