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 " . ______________________________________________________
