Question

What is the equation of the line that passes through the point `(1,5)` and is perpendicular to the graph of `x+2y=4`?

Answer 1

`y=1/2x+4.5`

Explanation:

First, we must solve `x+2y=4` for `y` (there is more than one way to do this.)

lets subtract `x` from both sides so we can get `2y=-x+4`

now we divide divide all terms by 2 to get `y` by itself.

our equation should now be `y=-2x+2`

Any question that asks you for a line perpendicular to another, you should know that the slope of the new line will be the negative reciprocal of the slope given.

In your case the opposite of `-2x` is `-1/2x` and then we multiply this by a negative, to get `1/2x`

From here, you have enough information to solve the problem using point slope form. which is `y-y1=m(x-x1)`

Now we plug in what we are given: `y1` is 5 (from the point given in the question), `m` is our new slope, `1/2x` and `x1` is 1 (from the point given in the question)

Now, our equation should be `y-5=1/2(x-1)`

Next, we distribute `1/2(x-1)` to get `1/2x-1/2`

By this point, our equation is `y-5=1/2x-1/2`

our LAST step is to add `5` to both sides.

We get `y=1/2x+4 1/2` which is the same as `y=1/2x+4.5`