Which equation represents line E, shown in the accompanying diagram? A.)y=2x+3
B.)y=1/2x+3
C.)y=3x+1/2
D.)y=3x+2
Please help

First, find the slope:

The slope is 1/2.

Now we have this much of the equation:

y = 1/2x + b

Plug in the point (0,3) to find the value of b

3 = (1/2)(0) + b

b = 3

Your final equation is y = 1/2x + 3.

Step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4