## Equations of lines

Consider the line with gradient 3 and *y*-intercept 2. This passes through the point *A*(0, 2). Let *B*(*x*, *y*) be any point on this line.

The gradient of the line is 3.

\begin{align}\text{So} \dfrac{y − 2}{x}&= 3\\ \text{Rearranging} y − 2 &= 3x\\ y &= 3x + 2\end{align}So the coordinates of *B*(*x*, *y*) satisfies *y* = 3*x* + 2. This is called the **equation of the line**.

Conversely, suppose that *B*(*x*, *y*) satisfies the equation *y* = 3*x* + 2, then = 3 and it passes though the point (0, 2) so the point lies on the line with gradient 3 and *y*-intercept 2.

*y*= 3

*x*+ 2.