Answer:
y = - 3x + 6
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange x - 3y = 5 into this form
Subtract x from both sides
- 3y = - x + 5 ( divide all terms by - 3 )
y = [tex]\frac{1}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{1}{3}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{1}{3} }[/tex] = - 3
Note the line crosses the y- axis at (0, 6) ⇒ c = 6
y = - 3x + 6 ← equation of perpendicular line
