Find the equation of the straight line that is parallel to \(y = 4x - 1\) and passes through the point \((0,6)\).

Two facts fix a straight line in the form \(y = mx + c\): its gradient \(m\) and its \(y\)-intercept \(c\).

Parallel lines have the same gradient, because they slope at the same angle and never meet. The line \(y = 4x - 1\) has gradient \(4\), so the new line also has gradient \(=4\) [B1].

The point \((0,6)\) has \(x=0\), so it lies on the \(y\)-axis and is therefore the \(y\)-intercept itself, giving \(c = 6\). Putting the two together, the equation is \(y = 4x + 6\) [B1].

The value of \(c\) can also be found by substituting: \(6 = 4 \times 0 + c\) gives \(c = 6\). Note that only the constant changes between parallel lines. Keeping the \(-1\) from the original equation, or changing the \(4\), would produce a line that is either not parallel or does not pass through the given point.