Examples. The gradient of a line inclined at an angle of \(45^0 \) is \(m = tan 45^0 = 1 \) The gradient of a line joining the points(0, 3) and (1, 5) is \(m = \frac{5 - 3}{1 - 0} = \frac{2}{1} = 2 \) The gradient of the tangent to the curve \(y = x^2 + x + 3 \) is \(\frac{d}{dx}.y = \frac{d}{dx}.(x^2 + x + 3)\) =\( 2x + 1 + 0 = 2x + 1 \)

gradient = height ÷ width; Example. The triangle goes from 2 to 8 on the (text{y})-axis, so has a height of 6. It goes from 1 to 3 on the (text{x})-axis, so has a width of 2.