[tex]\textsf{Let y = ax + b the line we want to find.}[/tex]
[tex]\textsf{We know that the slope of y = ax + b is the inverse of the slope of } \mathsf{ y = \frac{1}{4}x - 2.}[/tex]
[tex]\textsf{Thus:}[/tex]
[tex]\mathsf{a = \dfrac{1}{\frac{1}{4}} = 4}[/tex]
[tex]\textsf{As y = 4x + b passes thought (5, -2):}[/tex]
[tex]\mathsf{-2 = 4 \cdot 5 + b \Rightarrow 20 + b = -2 \Rightarrow b = -22}[/tex]
[tex]\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).}[/tex]
The equation of the line that is perpendicular to (y = 1/4 x – 2) and passes through the point (5, -2) is (y + 4x = 18).
Given :
The line that is perpendicular to y = 1/4 x – 2 and passes through the point (5, -2).
The following steps can be used in order to determine the equation of a line that is perpendicular to y = 1/4 x – 2 and passes through the point (5, –2):
Step 1 - The one-point slope form can be used in order to determine the equation of a line that is perpendicular to y = 1/4 x – 2 and passes through the point (5, –2).
Step 2 - The one point-slope form is given below:
[tex](y-y_1)=m(x-x_1)[/tex]
Step 3 - The slope of the line which is perpendicular to the line y = 1/4 x – 2 is:
[tex]m\times \dfrac{1}{4}=-1[/tex]
m = -4
Step 4 - So, the equation of a line that passes through the point (5,-2) and has a slope -4 is given below:
[tex](y+2)=-4(x-5)[/tex]
Step 5 - Simplify the above expression.
y + 4x = 18
For more information, refer to the link given below:
https://brainly.com/question/2564656
