Answer: The slope is: -1 .
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Explanation:
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We are given the equation: 3x + 3y = 63 ;
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in "standard form" ; that is: ax + by = c ;
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To find the "slope" of this equation, or slope of the line formed by this equation (which is a linear equation, in the format: "ax + by = c" ;
we can rewrite the equation in: "slope-intercept format"; or:
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y = mx + b ;
in which:
"y" stands alone as a single, "positive 1" (implied coefficient) on the "far left-hand side" of the equation,
"m" is the coefficient of "x"; and "m" is the "slope"—and is the value for which we wish to solve.
"b" is the "y-intercept", which is the point where the graph of the line crosses the y-axis ;
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So, given: "3x + 3y = 63" ; let's convert to: "y = mx + b" ; that is, "slope-intercept format"; to determine that value of "m" (the slope).
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→ Given: 3x + 3y = 63 ;
→ Let us divide BOTH sides of the equation by "3", to simplify matters:
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→ {3x + 3y} / 3 = 63 / 3 ; to get:
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→ x + y = 21 ; Now, let us subtract "x" from EACH side of the equation; to isolate "y" on one side of the equation:
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→ x + y − x = 21 − x ; → to get: y = 21 − x ;
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→ We have: y = 21 − x ; we need to write in the format of: "y = mx + b" ;
We already have "y" on the left-hand side of the question;
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So we take the "right-hand side" of the equation, and we take the term:
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→ 21 − x ; and rewrite as: 21 + -x ; and then rewrite as: -x + 21 ;
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→ Then, we can rewrite the entire equation in the format of:
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y = mx + b ; → y = - x + 21 ; in which "m" (the slope) = - 1 (implied coefficient), and b = 21.
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Since "m = -1 ", the slope = -1 ; which is our answer.
