Which is the graph of 2x - 4y > 6? 4
TY
417
41Y
N
2.
N
N
a
2
4
2
4 -2
-2
-4 -2
-2
2
-4-2
2
AN
-2
X

Step-1: the x-intercept and the y-intercept

2x - 4y = 6

For y = 0, we get the x-intercept.

2x - 4(0) = 6

2x = 6, and then divide by two on both sides.

Hence, the x-intercept is

For x = 0, we get the y-intercept.

2(0) - 4y = 6

-4y = 6, and then divide by -4 on both sides.

Hence, the y-intercept is y = -3/2 = ( 0, -3/2)

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