The general equation appears as \(Ax + By + C = 0\).

However to build up an equation use \(y - b = m(x - a)\) where \(m\) is the gradient and \((a,b)\) is a point on the line.

Find the equation of the line with gradient 3, passing through \((4,1)\).

Using \(y - b = m(x - a)\) with \(m = 3\) and \((a,b) = (4,1)\), we get:

\(y - 1 = 3(x - 4)\)

\(y - 1 = 3x - 12\)

\(y = 3x - 11\)

\(3x-y-11=0\)

To identify features compare with the form \(y = mx + c\) where \(m\) is the gradient and \((0,c)\) is the y-intercept.

Find the gradient of the line with equation \(2x + 5y - 6 = 0\)

Rearrange this in the form \(y = mx + c\) to get:

\(2x + 5y - 6 = 0\)

\(5y = - 2x + 6\)

\(y = - \frac{2}{5}x + \frac{6}{5}\)

\(gradient = - \frac{2}{5}\)