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 -[tex] \frac{1}{2} [/tex], 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:
[tex]y[/tex] - [tex] y_{1} [/tex] = [tex]m[/tex]([tex]x[/tex] - [tex] x_{1} [/tex]
We then substitute in the gradient and given coordinates to get:
[tex]y[/tex] - 7 = -[tex] \frac{1}{2} [/tex]([tex]x[/tex] - 4)
2y - 14 = x - 4
2y = x + 10
y = [tex] \frac{1}{2} [/tex]x + 5
