Answer: [C]: " 7x − 4y = 4 " .
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Explanation:
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We are given the following equation:
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" y = (7/4) x − 3 " ; which is in "slope-intercept form"; that is:
"y = mx + b " ; in which "m" = the slope = "(7/4)" .
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Among the answer choices given,
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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]:
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" 7x − 4y = 4" ; is written in "slope-intercept form;
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we get: -4y + 7x = 4;
-4y = 4 -7x = -7x +4;
-4y = -7x + 4 ;
Now, divide EACH side of the equation by "-4" ;
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-4y / -4 = (-7x + 4) / -4 ;
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To get:
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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.
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