Question

Write y=2/3x+7 in standard form,

Answer 1

The answer is: [A]: -2x + 3y = 21 .
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Note that "standard form" refers to:
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→  Ax +By =C ;
      in which "x" and "y" are variables; "A" and "B" represent the coefficients before those variables, respectively; and "C" is a number (not a variable).
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I shall demonstrate 2 (two) methods to convert the equation given:
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→  y = (⅔) x + 7 ;   to "standard form".).
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Method 1:
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→ Given: y = (⅔)x + 7 ; 
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→ Subtract "y" from EACH SIDE of the equation; and subtract "7" from EACH SIDE of the equation. Doing so: 1) puts the "x" and "y' values on one side of the equation; 2) removes a numeric value from the side of the equation with the "x" and "y" values; and 3) puts a numeric value on a side of the equation that does not have any "x" or "y" values — all three of which help to convert to equation to "standard form"—that is, " Ax + By = C " ;
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→ y = (⅔)x + 7 ;  → y − y − 7 = (⅔)x + 7 − y − 7 ; To get:
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→  -7 = (⅔)x − y  ↔ Rewrite as: (⅔)x − y = -7 ;
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Note:  While this very would could be an answer in"standard form"; 
 "Ax + By = C", in which A = ⅔ , B = -1; and C = -7; 
                     (Note: There is an implied "1" before the "y", since  "1*y = y; 
                                    since: y*1 = y; (anything * 1 = said number); 
                                     and the coefficient is "-1" (NEGATIVE 1); since the                                               "standard form" is: "Ax + By = C; and we have: 

                                                                             (⅔)x − y = -7 ; so the:
"− y" functions as a: PLUS "negative 1y"; in this circumstance.
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However, this equation—as written—does NOT match any of the answer choices given.
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→So, now we should multiply our ENTIRE equation (BOTH SIDES) by "-3"; for the sake of:  
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1) getting an answer choice that matches one of the answer choices given;
AND: 
2) for the general sake of simplicity—which would include getting the "-7" changed to a "positive 21" ;
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 → {Note: A non-zero, negative integer, when multiplied by another non-zero, negative integer; will result in a non-zero POSITIVE integer.
 As such: -7 *-3 = 21}.
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We have:  (⅔)x − y = -7 ; We shall multiply EACH SIDE of the equation by "-3";     → -3 * {(⅔)x − y = -7} ;
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→  Note: Start with:
   →"(-3 * (⅔)x =  -3 * ⅔ * x ;
   →   -3 * ⅔  = $\frac{-3}{1}$ * $\frac{2}{3}$  =(-3*2)/(1*3)
= -6 / 3 = -2 ;  → Don't forget to bring down the "x":  -2 * x = -2x ; 
→ So: - 3 *(⅔)x = - 2x ;
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The next term: -3 *-1y = +3y ; (Note: -3 *-1y = (-3* -1)*y = 3*y = +3y ;
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The next term: -3*(-7) = +21 ;
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→ to get:  → -2x + 3y = 21 ; which is: 'Answer choice: [A]'.
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Method 2:
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Given: y = (⅔)x + 7 ; write in standard form:
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 →  Given:    y = (⅔)x + 7 ; Multiply EACH SIDE of the equation by "3", to get rid of the fraction, "(⅔)" ; 
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 → 3* { y = (⅔)x + 7 } ;  to get:
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First term: 3*y  = 3y;  

Second term: 3*((⅔)x)) = 3 * (⅔) * x ;  3 * (⅔) = (3/1)*(2/3) =(3*2)/(1*3) =
6/3 = 2; → Don't forget the "x" → 2 * x
    = 2x;
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Third term: 3*7 = 21;
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→To get: → 3y = 2x + 21 ; 
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 → Now, subtract "3y" and subtract "21" from EACH SIDE of the equation:
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→ 3y = 2x + 21 ;   →  3y − 21 − 3y = 2x + 21 − 3y − 21 ;
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to get: →  -21 = 2x − 3y ; → Rewrite as: → 2x − 3y = -21 ;

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Note:  This would appear in "standard form" equation; "Ax + By = C"; 
                       in which A = 2; B = 3; C = -21;
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However,  " 2x − 3y = -21 " ;  is NOT an answer choice given.
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However, there are answer choices given with "21" {note: "positive 21"} representing the number for "C" within the "standard form" equation: 
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→ "Ax + By = C"
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 So, given our equation:
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→ 2x − 3y = -21 ;
          → We can multiply the ENTIRE equation (BOTH sides) by "-1" ; to                 change the "-21" value to "21" (positive 21); and see if the equation matches any of the answer choices:
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→  -1 * {2x − 3y = -21} ; 
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First term:  -1* 2x = -2x ; 

Second term: -1 * -3y = -1 * -3 * y = +3y ; 

Third term: -1 * -21 = + 21
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→  -2x + 3y = 21 ; which is:   'Answer choice: [A]'.

Answer 2

I hope this helps you




y=2/3x+7.3/3.1


y=2x+21/3


3y=2x+21


3y-2x=21