Which equation describes the same line as y – 6 = –4(x + 1)?
a. y = –4x + 3
b. y = –4x + 2
c. y = –4x + 7
d. y = –4x – 4?

The correct answer is:  [B]:  " -4x + 2 " .

Explanation:

Method 1)

Given the equation for a line:

  "y – 6 = –4(x + 1) " ;  we are asked to choose
                    which equation  (from the answer choices provided) the describes the same line (on a graph); or, in other words,
        the same aforementioned equation,
        which is "given" (in this very question being asked).

Note:  All the FOUR (4) answer choices given are written in "slope-intercept form".

We want to convert this equation to, and rewrite this equation in,
"slope-intercept form" ;

which is:

" y = mx + b " ;
in which:"y" is a single, "stand-alone" variable on the "left-hand side of the equation"; "m" is the coefficient of "x" ;
Furthermore, "m" is the slope of the line;
"b" is the "y-intercept"; or more precisely, the value of "x"
          (that is; the "x-coordinate" of the point at which "y = 0" );
          that is, the value of "x" ; or the "x-coordinate" of the point at which
             the graph of the equation crosses the "x-axis".

So, given:   "y – 6 = –4(x + 1) " ;

Let us start by expanding the "left-hand side of the equation" ;

 that is:   " - 4(x + 1) " ;

Note the "distributive property" of multiplication:

a(b + c) = ab + ac ;a(b – c) = ab – ac .

→  So;  -4(x + 1) =  -4*x  + (-4)*(1)  =  -4x + (-4)  = -4x  –  4 ;

→ Rewrite the equation:

y – 6 = –4(x + 1) =

   → y – 6  = -4x – 4 ;

           Add "6" to EACH SIDE of the equation; to isolate "y" on the "left-hand side" of the equation ; and to write the equation in "slope-intercept form" ;

       →  y – 6  + 6  = -4x – 4 + 6 ;

to get:

           →  y = -4x + 2 ; which is: Answer choice: [B] .

Method 2).

The other formula for the equation of a line, given a particular point on that line;  
  " (x₁, y₁)" ;   is:  " y – y₁ = m(x  – x₁) " ; in which "m" is the slope of that line.

So, in the original equation in the question:

 "  y – 6 = –4(x + 1) " ;

  y₁ = 6
 m = -4

x₁ = - 1 (note: This is a NEGATIVE value, because of the right-hand side of the equation in the formula is:  "m(x – x₁)"  ;  is equal to: " –4(x + 1)" ;

So,  we and to make "x₁" negative, because "x - (-1)" = "(x+1)" ; in order to make it a positive value in the original equation.

So we now that "m = -4" ; which is the case in all the answer choices.

On the right-hand side of our equation:

  = -4(x +1) ; Use the distributive property: 
                        -4(x + 1) = -4*x  + -4(1) =  -4x – 4 ;

  y – 6 = -4x – 4    ;

Add "6" to both side of the equation; to isolate "y" on the left-hand side of the equation:

 y – 6 + 6  = -4x – 4 + 6 ;

 to get:

          y = -4x + 2  ; which is: Answer choice: [B] .
.              

Where the white dots are is where your points should be plotted.a translation is simply just moving something from one place to another. in this case, you would move each plot point of the original shape 2 units up, and 5 units to the left.

The graph isn’t that clear