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 " . ______________________________________________________
She burned 30 calories for each minute of jogging and 15 calories for each minute of cycling because 300 divided by 10 is 30 and 300 divided by 20 is 15
