The answer is: [C]: " y = 3x + 2 " .
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Explanation:
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In "slope-intercept form" ; the equation is written in the following form:
" y = mx + b " ; with the "y" as a single variable on the "left-hand side" of the equation; and "m" is slope of the line and coefficient of "x" ; and "b" is the "y-intercept" (or more precisely, the coordinate of "x" when "y = 0").
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Answer choice: [C]: " -3x + y = 2 " ; written in slope-intercept is as follows.
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Given: -3x + y = 2 ; add "3x" to EACH side of the equation ; to isolate "y" as a single variable on the "left-hand side of the equation ;
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-3x + y + 3x = 2 + 3x ;
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to get: y = 2 + 3x ; rewrite as:
↔ " y = 3x + 2 " ;
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and the equation is in "slope-intercept form" ; that is:
" y = mx + b " ;
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in which the slope, "m", equals "3" ; and the point: "(1, 5)" is included.
{that is ; when "x = 1, y = 5 "} ;
→ y = 3x + 2 ; 3(1) + 2 = 3 + 2 = 5 .
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