Question

A straight 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

Answer 1

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 -
`(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 = -
`(1)/(2)`(
`x` - 4)

2y - 14 = x - 4
2y = x + 10
y =
`(1)/(2)`x + 5