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What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)​

User Alexhayes
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1 Answer

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Answer: y = ⁵/₂ x - 13 OR y + 8 = ⁵/₂ x - 5

Explanation:

Find the slope of the perpendicular line

When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.

⇒ if the slope of this line = - ²/₅

then the slope of the perpendicular line (m) = ⁵/₂

Determine the equation

We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:

⇒ y - (-8) = ⁵/₂ (x - 2)

y + 8 = ⁵/₂ (x - 2)

We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:

since y + 8 = ⁵/₂ (x - 2)

y = ⁵/₂ x - 13

What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)​-example-1
User Separius
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