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Finding equation of the line that is perpendicular to given one

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

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: $y=-\frac{1}{4}x+7$

2020-11-29