Write y = 1/8x+7 in standard form using integers. a –x + 8y = 7 b –x + 8y = 56 c 8x – y = 56 d –x – 8y = 56

The answer is:  [D]:  " - x − 8y = 56 " .

Explanation:

The "standard form" is:  "Ax + By = c" .

 Given:  " Y = 1/8 x + 7 " ; 

 ↔  "(1/8)x + 7 = y " ;

Subtract "7" from each side of the equation; & subtract "y" from each side of the equation :

     →   (1/8)x + 7 − 7 − y = y − 7 − y ; 

to get:  

     →   (1/8)x − y = - 7 ;

Now, multiply EACH side of the equation by "-8" ; to get rid of the FRACTION (since we want the "standard form" equation in INTEGERS;  and use "NEGATIVE 8" to get ride of the "-7" ;  since the "negative 7" multiplied by a "negative integer" will result in a POSITIVE INTEGER ;

    →   -8 * {(1/8)x − y }  = -8* {-7} ; 

To get:

    →  " - x − 8y = 56 " .

The answer is:  [D]:  " - x − 8y = 56 " .

 Note:  This is in "standard form" ; that is;  "Ax + By = C" ; 
             in which:  " A = -1 ; B = -8 ;  C = 56 " .

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