Answer:
Option 3 - [tex]y=-6x+28[/tex]
Step-by-step explanation:
Given : Perpendicular to the line [tex]x - 6y = 8[/tex]; containing the point (4,4).
To Find : An equation for the line with the given properties ?
Solution :
We know that,
When two lines are perpendicular then slope of one equation is negative reciprocal of another equation.
Slope of the equation [tex]x - 6y = 8[/tex]
Converting into slope form [tex]y=mx+c[/tex],
Where m is the slope.
[tex]y=\frac{x-8}{6}[/tex]
[tex]y=\frac{x}{6}-\frac{8}{6}[/tex]
The slope of the equation is [tex]m=\frac{1}{6}[/tex]
The slope of the perpendicular equation is [tex]m_1=-\frac{1}{m}[/tex]
The required slope is [tex]m_1=-\frac{1}{\frac{1}{6}}[/tex]
[tex]m_1=-6[/tex]
The required equation is [tex]y=-6x+c[/tex]
Substitute point (x,y)=(4,4)
[tex]4=-6(4)+c[/tex]
[tex]4=-24+c[/tex]
[tex]c=28[/tex]
Substitute back in equation,
[tex]y=-6x+28[/tex]
Therefore, The required equation for the line is [tex]y=-6x+28[/tex]
So, Option 3 is correct.
