What is the equation of a line perpendicularto y=-2/5x-1 that passes through(2,-8)
1 answer:
<h2>Answer: y = ⁵/₂ x - 13 OR y + 8 = ⁵/₂ x - 5 </h2><h3>Step-by-step explanation:</h3>
<u>Find the slope of the perpendicular line</u>
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are <em>negative-reciprocal</em>s of each other.
⇒ if the slope of this line = - ²/₅
then the slope of the perpendicular line (m) = ⁵/₂
<u>Determine the equation</u>
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
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