Question

A line is perpendicular to y =-1/3x +7

Answer 1

The equation of the perpendicular line is y = 3x – 10.

Solution:

Equation of the line:

$y=-\frac{1}{3}x+7$

Slope of this line,

$m_1=\frac{-1}{3}$

If two lines are perpendicular, then the product of their slopes equal to –1.

$\text{Slope of perpendicular line}=\frac{-1}{\text{Slope of the line} }$

$\Rightarrow m_2=\frac{-1}{m_1 }$

$\Rightarrow m_2=\frac{-1}{\frac{-1}{3} }=\frac{3}{1}$

$\Rightarrow m_2=3$

The line passes through the point (4, 2).

Here, $x_1=4, y_1=2$

Point-slope formula:

$y-y_1=m(x-x_1)$

$y-2=3(x-4)$

$y-2=3x-12$

Add 2 on both sides of the equation.

y = 3x – 10

The equation of the perpendicular line is y = 3x – 10.