Answer:
[tex]y = -3x + 14[/tex]
Step-by-step explanation:
Required
The equation of line
perpendicular to : [tex]x -3y =9[/tex]
Passes through [tex](3,5)[/tex]
We have:
[tex]x -3y =9[/tex]
Make y the subject
[tex]3y =x - 9[/tex]
Solve for y
[tex]y = \frac{x}{3} - 3[/tex]
Compare the above equation to [tex]y = mx + c[/tex]
[tex]m =\frac{1}{3}[/tex] ---- This represents the slope
Since the line is perpendicular to [tex]x -3y =9[/tex], then its slope is:
[tex]m_2 = -\frac{1}{m}[/tex]
[tex]m_2 = -\frac{1}{1/3}[/tex]
[tex]m_2 =-3[/tex]
The equation of the perpendicular line is:
[tex]y =m_2(x - x_1) + y_1[/tex]
Where:
[tex]m_2 =-3[/tex]
[tex](x_1,y_1) =[/tex] [tex](3,5)[/tex]
So:
[tex]y = -3(x - 3) + 5[/tex]
[tex]y = -3x + 9 + 5[/tex]
[tex]y = -3x + 14[/tex]