The slope of a line is -1/3, and the y-intercept is 10/3. what is the equation of the line written in general form? 10x + 3y - 1 = 0 x + 3y + 10 = 0 x + 3y - 10 = 0

The answer is:  [B]:  " x  + 3y + 10 = 0 " .

Explanation:

Note the equation for a line; in 'slope-intercept form':  "y = mx + b" ;
 
   in which "y" is isolated alone, as a single variable, on the left-hand side of the equation;
                "m" = the slope of the line; and is the co-efficient of "x" ;
                                  b = the "y-intercept"; (or the "y-coordinate of the point of                                                                          the "y-intercept"). 

So, given the information in this very question/problem:

slope = m = (-1/3) ; 
b = y-intercept = (10/3) ; 

And we can write the equation of the line; in "slope-intercept form"; that is:

  " y = mx + b " ;  as:


   " y = (-1/3)x + (10/3) " ;

Now, the problem asks for the equation of this line; in "general form";  or "standard format";  which is:

   "Ax + By + C = 0 " ; 

So; given: 

 " y = (-1/3)x + (10/3) " ;

  We can multiply the ENTIRE EQUATION (both sides) by "3" ; to get rid of the "fractions" ;

  →  3* { y = (-1/3)x + (10/3) } ;

  →  3y = -1x + 10 ; 

        ↔  -1x + 10 = 3y ; 

Subtract "(3y)" from each side of the equation:

            -1x + 10 − 3y = 3y − 3y ;

to get: 

-1x + 10 − 3y = 0 ; 

↔  -1x − 3y − 10 = 0 ;  

→ This is not one of the "3 (THREE) answer choices given" ;

→ So, multiply the ENTIRE EQUATION (both sides); by "-1" ; as follows:

     -1 * {-1x − 3y − 10 = 0} ; 

to get:

   →   " x + 3y + 10 = 0 " ;  which is:  "Answer choice:  [B] ."

Note that is equation is in the "standard format" ;
   →  " Ax + By + C = 0 " .