I don't understand how to write an equation with a perpendicular line. The book does not have an example.

Write and equation of aline through (4, 5) that is perpendicular to y=1/2x & 3.

I have been doing equations when there are two sets of ordered pairs. This only has 1.

Please help.
Thanks

Two lines are perpendicular if the product of their gradients is -1

Ie. M_1 * m_2 = -1
Where m_1 = gradient of first line
M_2 = gradient of 2nd line

The line you have is of gradient 1/2, so a line perpendicular to that would have gradient -2

Then it goes through (4,5) you said,

So using the equation
Y-5 =(-2) (x-4)

You get the answer

Well to get a perpendicular slope, do the inverse recipricle of the regular slope, in this case 1/2 inverse: -1/2 and then the reciprical -2. Once you have the slope rewrite the equation in the y=mx + b form. Y=-2x + 3, and the other order pair is (0,3) and this is because the y-intercept is 3. X:4-0=4 and y:5-3=2, so the equations should be set up: y-2=-2(x+4)+3, or y-2=(-2x-8)=3.