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