Which line is parallel to the line through (-3, 3) and (3, 7) line 1: through (3, -2) and (-4, -8) line 2: (0, -7) and (-6, -11)

 The answer is:  [B]:  " Line 2:  (0, -7) and (-6, -11) " .  

  " Line 2" is parallel to [ the line through (-2, 3) and (3, 7) .

Explanation:

The line given in the question:

described as a line through (-3,3) and (3,7).

Let's refer to this coordinates as (x₁, y₁) and (x₂, y₂) ;

in which:  "x₁ = -3;  y₁ = 3 ;  x₂  = 3 ; y₂ =7" ;

Let us calculate the slope of this line:

The slope: "m" = (y₂ − y₁) / (x₂ − x₁) ;  Plug in our known values;

                        = (7 − 3) / [(3 − (-3) ] = 4 / (3+3) = 4/6  = 2/3 ; 

Note: We are asked, "Which line is parallel to [this line]?" ;  and we are given TWO (2) answer choices.  Note that lines that are parallel to one another have the same "slope" .

Let us try the first answer choice:  

 [A]:  "Line 1" — passes through (3, -2) and (-4, -8).

Let's refer to this coordinates as (x₁, y₁) and (x₂, y₂) ;

in which:  "x₁ = 3;  y₁ = -2 ;  x₂  = - 4 ; y₂ = -8" ;

Let us calculate the slope of this line:

The slope: "m" = (y₂ − y₁) / (x₂ − x₁) ;  Plug in our known values;

                        = [(-8 − (-2)] / (-4 − 3) = (-8 + 2) / -7) = -6/-7 = 6/7 .

The slope of this line, "Line 1" is:  "6/7"; which does NOT equal "2/3"; so "Line 1" is NOT parallel to [the line described in this very question].

The answer should be "Line 2" ; but let us make sure:

 [B]:  "Line 2" — passes through (0, -7) and (-6, -11).

Let's refer to this coordinates as (x₁, y₁) and (x₂, y₂) ;

in which:  "x₁ = 0;  y₁ = -7 ;  x₂  = -6 ; y₂ = -11" ;

Let us calculate the slope of this line:

The slope: "m" = (y₂ − y₁) / (x₂ − x₁) ;  Plug in our known values;

                        = [(-11 − (-7)] / (-6 − 0) = (-11+7) / -6) = -4/-6 = 4/6 = 2/3 .

The slope of this line, "Line 2" is:  "2/3"; which is the same slope as the slope of the line described in this very question;  so "Line 2" IS PARALLEL TO the line described in the question.

The answer is:  [B]:  " Line 2:  (0, -7) and (-6, -11) " .