Answer:
The required equation is [tex]y=-\frac{1}{3}x+2[/tex].
Step-by-step explanation:
The equation of line cd is
[tex]y=3x-3[/tex]
Slope intercept form of a line is
[tex]y=mx+b[/tex]
Where, m is slope and b is y-intercept.
Slope of line cd is 3.
The product of slopes of two perpendicular lines is -1.
[tex]m_1\times m_2=-1[/tex]
[tex]3\times m_2=-1[/tex]
[tex]m_2=-\frac{1}{3}[/tex]
Therefore slope of perpendicular line is [tex]-\frac{1}{3}[/tex].
Point slope form of a line is
[tex]y-y_1=m(x-x_1)[/tex]
Slope of perpendicular line is [tex]-\frac{1}{3}[/tex] and line passing through the point (3,1).
[tex]y-1=-\frac{1}{3}(x-3)[/tex]
[tex]y=-\frac{1}{3}x+1+1[/tex]
[tex]y=-\frac{1}{3}x+2[/tex]
Therefore the required equation is [tex]y=-\frac{1}{3}x+2[/tex].
