The correct answer is: [A]: " x + 2y = -11 " . ________________________________________________ Explanation: _________________________________________________ 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 ; ______________________________________________ Divide EACH SIDE of the equation by "2" ; ______________________________________________ 2y / 2 = (-1x − 11) / 2 ;
to get: y = (-1/2)x − (11/2).
So: Answer choice: [A]: should be the correct answer . ______________________________________________ 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. _________________________________________________________ So the correct answer is: Answer choice:[A]: " x + 2y = -11 " . _________________________________________________________
