Which equation represents a line that is parallel to the line $y = 3 - 2 x$ $y=3- 2x$ ?

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Which equation represents a line that is parallel to the line $y = 3 - 2 x$ $y=3- 2x$ ?

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Answer 1 · 2016-12-28T14:03:22

$y = k - 2 x$ $y=k-2x$ , where $k \neq 3$ $k!=3$ .

Explanation:

A line parallel to $a x + b y + c = 0$ $ax+by+c=0$ is of the type $a x + b y + k = 0$ $ax+by+k=0$ , where $k \neq c$ $k!=c$ . Note this means that only constant term changes. Note that in such cases slopes of both are same i.e. $- \frac{a}{b}$ $-a/b$ .

Hence equation of a line parallel to $y = 3 - 2 x$ $y=3-2x$ is $y = k - 2 x$ $y=k-2x$ , where $k \neq 3$ $k!=3$ .

Note: A line pperpendicular to $a x + b y + c = 0$ $ax+by+c=0$ is of the type $b x - a y + k = 0$ $bx-ay+k=0$ . Note this means that coefficients of $x$ $x$ and $y$ $y$ are interchanged and relatively their sign changes. Note that in such cases slopes of both are $- \frac{a}{b}$ $-a/b$ and $\frac{b}{a}$ $b/a$ and their product is $- 1$ $-1$ .

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Which equation represents a line that is parallel to the line $y = 3 - 2 x$ $y=3- 2x$ ?

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Explanation:

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Which equation represents a line that is parallel to the line y=3−2xy=3- 2x?

1 Answer

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Which equation represents a line that is parallel to the line $y = 3 - 2 x$ $y=3- 2x$ ?