# Finding equation of the line that is perpendicular to given one

Find the equation of the line that is perpendicular to y = 4x - 1 and passes though the point (8,5)?

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General equation of the straight line is $y=mx+c$. Characteristic of perpendicular straight lines slopes: $m_1\cdot m_2=-1$. Now we can find the lope of our equation: $$m\cdot 4 = -1, \ \ m=-\frac{1}{4}$$ If $m=-\frac{1}{4}$, then we have $y=-\frac{1}{4}x+c$. Now we can easy find c by inserting given point coordinates to our equation. $$5=-\frac{1}{4} \cdot 8 + c, \ \ c=7$$ Answer: $y=-\frac{1}{4}x+7$

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