Write an equation of the line in slope intercept from given the following information, then sketch it's graph. 1. The point (5, -4) and slope -1/2 2. Points ( -3,4) and (5, 8) 3. Horizontal line passing through the point (2, -7) 4. The line perpendicular to x+y= 5 through the point (2, -3)

30005

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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

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