The correct answer is: [D]: " y = - 4x − 13 " . ______________________________________________ Explanation: _____________________________________________________
All the answer choices given are written in "point-slope format" (also known as "slope-intercept format" — that is: " y = mx + b" .
All of the answer choices given have a slope of "-4" ; that is: "m = -4" . _____________________________________________________ The only answer choice with the equation that passes through point "(-3, 1)" — that is, when "x = -3, y = 1" — is: ___________________________________________________ Answer choice: [D]: " y = - 4x − 13 " . ___________________________________________________ In the equation: " y = - 4x − 13 " ; when "x = - 3, y = 1" . ____________________________________________________ Given: " y = - 4x − 13 " ;
↔ - 4x − 13 = y ;
Plug in "(-3)" for "x" ; and see that "y = 1" ;
-4(-3) − 13 = y ;
12 − 13 = y = -1 ; ______________________________ So, when x = -3, y = 1 . _________________________________________ The correct answer is: [D]: " y = - 4x − 13 " . ___________________________________________ Consider choice: [A]: " y = - 4x + 13 " ; Substitute "(-3)" for "x" and see if "y = -1" ; -4(-3) + 13 = y ; 12 + 13 = 25 ; NOT "-3" . ______________________________________ Consider choice: [B]: "y = - 4x + 7 " ; Substitute "(-3)" for "x" and see if "y = -1" ; -4(-3) + 7 = y ; 12 + 7 = 19 ; NOT "-3" . ______________________________________ Consider choice: [C]: " y = - 4x − 7 " ; Substitute "(-3)" for "x" and see if "y = -1" ; -4(-3) − 7 = y ; 12 − 7 = 9 ; NOT "-3" . ___________________________________________ This leaves us with "Answer choice: [D]: " y = - 4x − 13 " ; the only remaining answer choice; which we have already confirmed is correct; so we do not need to check. _______________________________________________ Hope this helps! ______________________________________________
