Answer:
[tex]y = (\frac{-1}{6})x - 3[/tex]
Step-by-step explanation:
Given line = 30x - 5y = 5 or y = 6x + 1
so, the slope of the given line is 6.
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
⇒ 6(m) = -1
⇒ m = [tex]\frac{-1}{6}[/tex]
By substitutiong the value of m in the equation, we get;
⇒ [tex]y = (\frac{-1}{6})x + c[/tex]
For c,
as the point (0,-3) passes through the line, we get;
⇒ [tex]-3 = (\frac{-1}{6})(0) + c[/tex]
⇒ [tex] c = -3 [/tex]
Hence,
The line which is perpendicular to the given line and passes through (0,-3) is [tex]y = (\frac{-1}{6})x - 3[/tex] .
