Question

Find the equation of the straight line which has a gradient of -2 and passes through the point A(-1,3)

Answer 1

EXPLANATION.

Equation of straight lines,

Gradient = slope of line = -2.

Passes through the point (-1,3).

As we know that,

Equation of straight lines,

⇒ (y - y₁) = m(x - x₁).

⇒ ( y - 3) = -2(x -(-1)).

⇒ (y - 3) = -2(x + 1).

⇒ (y - 3) = -2x - 2.

⇒ y - 3 = -2x - 2.

⇒ y + 2x = 1.

                                                                                               

MORE INFORMATION.

(1) = Equation of straight lines through (x₁, y₁) and making an angle α with y = mx + c.

(y - y₁) = m ± tanα/1 ± m tanα (x - x₁).

(2) = Length of perpendicular from (x₁, y₁) to the straight line ax + by + c = 0 then,

p = | ax₁ + by₁ + c |/√a² + b².

(3) = Distance between two parallel lines.

ax + by + c₁ = 0  and  ax + by + c₂ = 0, then.

d = | c₁ - c₂ |/√a² + b².

Answer 2

$\large\underline{\red{\sf \pink{\bigstar} Correct\;Question}}$

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• Find the equation of the straight line which has a gradient of -2 and passes through the point A(-1,3)

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$\large\underline{\blue{\sf \orange{\bigstar} Solution:-}}$

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• Equation of straight lines,

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• Gradient = slope of line = -2.

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• Passes through the point (-1,3).

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☯ As we know that,

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$\pink{\sf{\star\;Equation \;of\; straight \;lines,}}$

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• ➦ (y - y₁) = m(x - x₁).

⠀⠀⠀⠀

• ➦ ( y - 3) = -2(x -(-1)

⠀⠀⠀⠀

• ➦ (y - 3) = -2(x + 1).

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• ➦ (y - 3) = -2x - 2.

⠀⠀⠀⠀

• ➦y - 3 = -2x - 2.

⠀⠀⠀⠀

⚛ ➦ y + 2x = 1.⚛

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