Answer: [tex]x+14y=109[/tex]
Step-by-step explanation:
Given
The line passes through [tex](-3,8)[/tex] and is perpendicular to the given line [tex]y=14x+12[/tex]
Comparing [tex]y=14x+12[/tex] with line [tex]y=mx+c[/tex] to get the slope i.e. [tex]\text{Slope=}14[/tex]
Suppose m is the slope of the required line
And the product of the slope of perpendicular lines is [tex]-1[/tex]
[tex]\therefore 14(m)=-1\\\\\Rightarrow m=-\dfrac{1}{14}[/tex]
The equation of the required line is
[tex]\Rightarrow \dfrac{y-8}{x+3}=-\dfrac{1}{14}\\\\\Rightarrow -14y+14\times 8=x+3\\\Rightarrow x+14y=112-3\\\Rightarrow x+14y=109[/tex]
None of the given options is correct.
