Answer:
[tex]y=5x + 8[/tex]
Step-by-step explanation:
Given line is [tex]y=(\frac{-1}{5})x + 9[/tex]
so, the slope of the given line is [tex]\frac{-1}{5}[/tex].
now, let the line which is perpendicular to the given line be y = mx + c
where,
m = slope of the line
c = constant
As we know, if two lines are perpendicular to each other, the value of product of there slopes are -1.
so, slope of given line × slope of perpendicular line = -1
⇒ [tex](\frac{-1}{5})m=(-1)[/tex]
⇒ [tex]m=5[/tex]
By substitutiong the value of m in the equation, we get;
⇒ [tex]y=5x + c[/tex]
For c,
as the point (-2,-2) passes through the line, we get;
⇒ [tex]-2=5(-2) + c[/tex]
⇒ [tex]c=8[/tex]
Hence,
The line which is perpendicular to the given line and passes through (-2,-2) is
[tex]y=5x + 8[/tex]
