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malfutka [58]
3 years ago
15

What is the slope of 2x+3y=15

Mathematics
1 answer:
Fynjy0 [20]3 years ago
5 0

Note that the slope-intercept form is: y = mx + b

First, set the equation as such

2x (-2x) + 3y = (- 2x) + 15

3y = -2x + 15

Isolate the y. Divide 3 from both sides

(3y)/3 = (-2x + 15)/3

y = (-2/3)x + 5

-2/3 is your slope

hope this helps

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The answer is:  [B]:  " x  + 3y + 10 = 0 " .
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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:
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   "Ax + By + C = 0 " ; 
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So; given: 
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 " y = (-1/3)x + (10/3) " ;
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  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:
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            -1x + 10 − 3y = 3y − 3y ;

to get: 

-1x + 10 − 3y = 0 ; 

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

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