Question

Find the equation of the line that is perpendicular to y = 1/4 x – 2 and passes though the point (5, –2).

Answer 1

$\textsf{Let y = ax + b the line we want to find.}$

$\textsf{We know that the slope of y = ax + b is the inverse of the slope of } \mathsf{ y = \frac{1}{4}x - 2.}$

$\textsf{Thus:}$

$\mathsf{a = \dfrac{1}{\frac{1}{4}} = 4}$

$\textsf{As y = 4x + b passes thought (5, -2):}$

$\mathsf{-2 = 4 \cdot 5 + b \Rightarrow 20 + b = -2 \Rightarrow b = -22}$

$\textsf{Hence the line y = 4x - 22 is perpendicular to }\mathsf{y=\frac{1}{4}x - 2}\textsf{ and passes for the point (5, -2).}$

Answer 2

Answer:

y=-4x+18

Step-by-step explanation: