The equation and intercepts of a line

In \(y=mx+c\), \(m\) is the gradient and \((0,c)\) is the \(y\)-intercept. Set \(y=0\) to find an \(x\)-intercept. A point lies on the line exactly when its coordinates satisfy the equation.

Example

For \(y=-2x+6\), the gradient is \(-2\). At \(x=0\), \(y=6\); at \(y=0\), \(x=3\). Thus the intercepts are \((0,6)\) and \((3,0)\).

The horizontal line \(y=4\) has gradient \(0\). The vertical line \(x=4\) cannot be written as \(y=mx+c\) with a finite gradient.