Show all work to write the equations of the lines, representing the following conditions, in the form y = mx + b, where m is the slope and b is the y-intercept:

Part A: Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0 (2 points)

Part B: Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0 (2 points)

Part A)

Part B)

Step-by-step explanation:

Part A) Passes through (−2, 2) and parallel to 4x − 3y − 7 = 0

we have

Isolate he variable y

The slope of the given line is

Remember that

If two lines are parallel then their slopes are the same

therefore

The slope of the line parallel to the given line is also

Find the equation of the line in slope intercept form

we have

substitute

solve for b

therefore

Part B) Passes through (−2, 2) and perpendicular to 4x − 3y − 7 = 0

we have

Isolate he variable y

The slope of the given line is

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

therefore

The slope of the line perpendicular to the given line is

Find the equation of the line in slope intercept form

we have

substitute

solve for b

therefore

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

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