(6,5), 7x-3y=5 find the equation of the line that contains the given point and is parallel to the line. write the equation in slope intercept form

y = (7/3)x - 9

Step-by-step explanation:

1. Convert given equation to y=mx+b form --> y = (7/3)x - 5/3

2. Equation of new line --> y = (7/3)x + b

3. Plug in given values --> 5 = (7/3)(6) + b

4. Solve for b --> b = 5 - 14    b = -9

5. New line --> y = (7/3)x - 9

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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