What is the slope of the graph of 6x + 2y = 14 in the... | SAT Linear equations in two variables Question, Answer Explained

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Math · AlgebraEasy

What is the slope of the graph of $6x + 2y = 14$ in the $xy$ -plane?

$-3$

$3$

$6$

$7$

Show answer and explanation

Answer: A

Solve for $y$ . Subtract $6x$ from both sides: $2y = -6x + 14$ . Divide by $2$ : $y = -3x + 7$ . The slope is the coefficient of $x$ , which is $-3$ .

Choice D, $7$ , is the $y$ -coordinate of the $y$ -intercept, not the slope.

Why the other choices are wrong

B. This forgets that moving 6x to the other side makes it negative: 2y = -6x + 14.
C. 6 is the coefficient of x before solving for y. Dividing by 2 and moving the term gives a slope of -3.
D. 7 is the y-intercept of y = -3x + 7, not its slope.

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