Point Slope Formula

The point slope formula allows you to calculate the equation of a line from a point on a line and its gradient. It’s given by the formula:

\[ y - y_0 = m(x - x_0) \]

Where \( m \) is the gradient of the line, \( y_0 \) and \( x_0 \) are the actual points sampled from the graph, and \(x \) and \( y \) are variables in the final equation.

This formula is derived from the standard slope \( \frac{dy}{dx} \) where:

\[ \frac{y - y_0}{x - x_0} = m \]

For example, if you have a graph with gradient of \( 3 \) and a point \( (3, 2) \) then this can be substituted into the point slope formula as:

\[ y - 2 = 3(x - 3) \]

So the equation of the line is:

\[ y = 3x - 7 \]