Answer: [C]: " 7x − 4y = 4 " .
_________________________________________________________
Step-by-step explanation:
_________________________________________________________
We are given the following equation:
_________________________________________________________
" y = (7/4) x − 3 " ; which is in "slope-intercept form"; that is:
"y = mx + b " ; in which "m" = the slope = "(7/4)" .
_________________________________________________________
Among the answer choices given,
________________________________
Answer choice: [C]: " 7x − 4y = 4 " ; is the only answer choice given which, when written in "slope-intercept form" ; that is: "y = mx + b" ; has a slope of "m = (7/4)". Specifically, when the given equation in answer choice [C]:
_________________________________________
" 7x − 4y = 4" ; is written in "slope-intercept form;
_________________________________________
we get: -4y + 7x = 4;
-4y = 4 -7x = -7x +4;
-4y = -7x + 4 ;
Now, divide EACH side of the equation by "-4" ;
_________________________________________
-4y / -4 = (-7x + 4) / -4 ;
_________________________________________
To get:
_________________________________________
y = (7/4) x + 1 ; and since the slope, "m = (7/4) is the same slope as the original equation, that this line (in answer choice 'C' is PARALLEL to the line in the original equation given.
______________________________________________