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

1 Answer
Dec 20, 2016

#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#