To find the equation of a line when given its gradient and a point it passes through, you can use the point-slope form of the equation, which is:
\[ y - y_1 = m(x - x_1) \]
where:
- \( m \) is the gradient of the line
- \( (x_1, y_1) \) is the point the line passes through
Given that the gradient is 2 and the line passes through the point (1, 4), you can substitute these values into the point-slope form to find the equation of the line.
1. Substituting the values into the formula:
\[ y - 4 = 2(x - 1) \]
2. Simplify the equation:
\[ y - 4 = 2x - 2 \]
\[ y = 2x + 2 \]
Therefore, the equation of the line with a gradient of 2 passing through the point (1, 4) is \( y = 2x + 2 \).
