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) " .
