If L is perpendicular to y = 2x + 3, we know that the gradient of L is the negative reciprocal of the gradient of y = 2x + 3, which is 2.
The negative reciprocal of 2 is -\(\frac{1}{2}\), and we know this because these two numbers multiply to make -1.
Now that we know the gradient of L, we use the following equation:
\(y\) - \(y_{1}\) = \(m\)(\(x\) - \(x_{1}\)
We then substitute in the gradient and given coordinates to get:
\(y\) - 7 = -\(\frac{1}{2}\)(\(x\) - 4)
2y - 14 = x - 4
2y = x + 10
y = \(\frac{1}{2}\)x + 5
