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3 years ago

What is the equation

Mathematics

1 answer:

katovenus [111]3 years ago

8 0

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") ;
_____________________________________________________
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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