Find the equation of the line parallel to y-8= 2/3x that passes through the point (-9-9)

y = (2x/3) - 3

Step-by-step explanation:

parallel means same slop

y=2x/3 + b

-9 = -6 + b

b = -3

therefore y = (2x/3) - 3

y = 2/3x - 3

Step-by-step explanation:

let's put equation into slope-intercept form first, which is y=mx+b where 'm' is the slope and 'b' is the y-intercept

y-8 = 2/3x

y = 2/3x+8

parallel lines have equal slopes, so we know our equation must have a slope of 2/3

now use (-9,-9) to find 'b':

-9 = 2/3(-9) + b

-9 = -6 + b

-3 = b

put it together:

y = 2/3x - 3

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