Question

What is the equation

Answer 1

The correct answer is:    [A]:  " x + 2y = -11 " .
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Explanation:
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First, we narrow down to choices:

         [A]:  "x + 2y = -11  ;  and:  [D]:  "2x + y = -10 " ;

since these are the only answer choices that the point "(-3, -4) pass through.

Now, write these in "slope-intercept form" (a.k.a. "point-slope form"); that is:

  y = mx + b ;

and see which one has the slope of "(-1/2)"  (i.e. "m = -1/2") ;
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Start with Answer choice  [A]:  "x + 2y = -11 " ;

                                               ↔ 2y + x = -11 ;
                                                 
                                            Subtract "x" from each side:
                                                    2y + x − x = -11 − x ;

                                            to get:  2y = -11 − x ; 
                                
                                               ↔   2y = -11 + (-x) ;
  
                                               ↔   2y = -x + (-11) ;

                                               ↔   2y = -1x − 11 ;
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Divide EACH SIDE of the equation by "2" ;
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                                            2y / 2  = (-1x − 11) / 2  ;
         
                                           to get:   y = (-1/2)x − (11/2).

So:  Answer choice:  [A]: should be the correct answer .
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Let us try Answer choice: [D] ;  just to rule out this possible answer:

                                                   " 2x + y = -10 " ;
                   
                                               ↔  y + 2x = -10 ;
                     
                                    Subtract "2x" from EACH SIDE of the equation ;

                                                    y + 2x − 2x = -10 − 2x ;
    
                                                               y = -10 − 2x ;
                 
                                                         ↔  y =  -10 + (-2x) ;

                                                         ↔  y = -2x + (-10) ;
          
                                                         ↔  y = -2x − 10 ;

                         The slope of: Answer choice [D]: is "-2" ;  NOT "(-1/2)".

So; we confirm that:  Answer choice: [D]:  is INCORRECT.
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So the correct answer is:  Answer choice:  [A]:  " x + 2y = -11 " .
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