Astraight line, l, passes through the point with the coordinates (4,7) and is perpendicular to the line with the equation y=2x+3. find an equation of the straight line l

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 -, 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:

-  = ( - 

We then substitute in the gradient and given coordinates to get:

- 7 = -( - 4)

2y - 14 = x - 4
2y = x + 10
y = x + 5