The equation of the perpendicular line is y = 3x – 10.
Solution:
Equation of the line:
[tex]$y=-\frac{1}{3}x+7[/tex]
Slope of this line,
[tex]$m_1=\frac{-1}{3}[/tex]
If two lines are perpendicular, then the product of their slopes equal to –1.
[tex]$\text{Slope of perpendicular line}=\frac{-1}{\text{Slope of the line} }[/tex]
[tex]$\Rightarrow m_2=\frac{-1}{m_1 }[/tex]
[tex]$\Rightarrow m_2=\frac{-1}{\frac{-1}{3} }=\frac{3}{1}[/tex]
[tex]$\Rightarrow m_2=3[/tex]
The line passes through the point (4, 2).
Here, [tex]x_1=4, y_1=2[/tex]
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2=3(x-4)[/tex]
[tex]y-2=3x-12[/tex]
Add 2 on both sides of the equation.
y = 3x – 10
The equation of the perpendicular line is y = 3x – 10.
