Line z passes through the points (-6, 2) and (-1, -4), as shown below. Which of the following could be the equation of a line that is parallel to line z? Select one or more:
A. y=−65x+10
B. y=65x−3
C. y=25x−1
D. y=x+4

Select one or more

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