Question

The slope of the line which is perpendicular to the line 3x+y=3 is
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Answer 1

Given line

• 3x + y = 3

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To find

• Slope of a line which is perpendicular to the given line.

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Solution

• Let us find the slope of the given line.

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$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {Write\: the\: equation\: in\: the\: form} \\ \bf\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {of\: \: \orange{y = mx + c}}$

→ y = -3x + 3

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Here,

• Slope of the line ($\sf{m_1}$) = -3

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★ We know that, when two lines are perpendicular to each other then product of their slopes is -1.

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• Let the required slope be $\sf{m_2}$.

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Therefore,

$\: \: \: \: \: \: \: \: \: \: \: \: \boxed{\tt{\bigstar{m_1 \times m_2 = -1{\bigstar}}}}$

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• We have

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$\tt\longmapsto{-3 \times m_2 = -1}$

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$\tt\longmapsto{m_2 = \dfrac{-1}{-3}}$

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$\tt\longmapsto{m_2 = \dfrac{1}{3}}$

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Hence,

• The required slope of the line is $\sf{\dfrac{1}{3}}$.

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