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?

2 answers:

6 0

The answer is: [B]: " x + 3y + 10 = 0 " .
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Explanation:
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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").
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So, given the information in this very question/problem:
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slope = m = (-1/3) ;
b = y-intercept = (10/3) ;
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And we can write the equation of the line; in "slope-intercept form"; that is:
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" y = mx + b " ; as:
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" y = (-1/3)x + (10/3) " ;
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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 ;

↔ -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:
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→ " x + 3y + 10 = 0 " ; which is: "Answer choice: [B] ."
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Note that is equation is in the "standard format" ;
→ " Ax + By + C = 0 " .
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