Answer:
[tex]y=\frac{-1}{6}x-\frac{10}{3}[/tex]
Step-by-step explanation:
Slope intercept form of the equation of a line is [tex]y=mx+b[/tex] where m denotes the slope of line and [tex]b[/tex] denotes the y-intercept.
Equation of a line u is [tex]y=6x+6[/tex]
Here, slope of line u = m = 6
As the line v is perpendicular to line u, product of slopes of both the lines is equal to [tex]-1[/tex].
Slope of line v [tex]=\frac{-1}{6}[/tex]
So, slope intercept form of the line v is [tex]y=\frac{-1}{6}x+b[/tex]
As point [tex](10,-5)[/tex] lies on the line v, put [tex](x,y)=(10,-5)[/tex] in equation [tex]y=\frac{-1}{6}x+b[/tex]
[tex]-5=\frac{-1}{6}(10)+b\\-5=\frac{-5}{3}+b\\ -5+\frac{5}{3}=b\\\frac{-15+5}{3}=b\\\\\frac{-10}{3}=b[/tex]
Equation of line v is [tex]y=\frac{-1}{6}x-\frac{10}{3}[/tex]
