Point-Slope Form Calculator

How to Calculate the Point-Slope Form of a Line

The point-slope form is a way to express the equation of a straight line using the slope of the line and a point on the line. It's particularly useful when you know the slope and a point, or when you want to find an equation of a line passing through two points.

Point-Slope Form Formula

The point-slope form of a line is given by the equation:

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

Where:

• m is the slope of the line
• (x₁, y₁) is a point on the line
• (x, y) represents any point on the line

Calculation Steps

1. Determine the slope (m) of the line. If you have two points, use the slope formula: m = (y₂ - y₁) / (x₂ - x₁)
2. Choose a point (x₁, y₁) on the line. If you're given two points, you can use either one.
3. Substitute the slope and the chosen point into the point-slope form equation: y - y₁ = m(x - x₁)
4. Simplify the equation if necessary

Example Calculation

Let's find the point-slope form of a line passing through the points (2, 3) and (5, 7).

1. Calculate the slope: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{7 - 3}{5 - 2} = \frac{4}{3} \]
2. Choose one of the points, let's use (2, 3)
3. Substitute into the point-slope form equation: \[ y - 3 = \frac{4}{3}(x - 2) \]
4. This is the point-slope form of the line

Visual Representation

A visual representation can help understand the concept better. Here's a diagram showing the line passing through the points (2, 3) and (5, 7):

This diagram illustrates the line in point-slope form y - 3 = (4/3)(x - 2), passing through the points (2, 3) and (5, 7).