Find the slope of the line passing through the points and .

slope = -

Step-by-step explanation:

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = (3, 8 ) and (x₂, y₂ ) = (7, - 7 )

m = = = -

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