# What is the equation of the line perpendicular to y=-25/3x  that passes through  (-1,-6) ?

May 8, 2018

Equation of the line is $3 x - 25 y = 147$

#### Explanation:

The slope of the line $y = - \frac{25}{3} x \left[y = m x + c\right]$

is ${m}_{1} = - \frac{25}{3}$ . The product of slopes of the perpendicular lines

is ${m}_{1} \cdot {m}_{2} = - 1 \therefore {m}_{2} = \frac{- 1}{- \frac{25}{3}} = \frac{3}{25}$

The slope of the line passing through $\left(- 1 , - 6\right)$ is $\frac{3}{25}$

The equation of line passing through $\left({x}_{1} , {y}_{1}\right)$ having slope of

$m$ is $y - {y}_{1} = m \left(x - {x}_{1}\right)$.

The equation of line passing through $\left(- 1 , - 6\right)$ having slope of

$\frac{3}{25}$ is $y + 6 = \frac{3}{25} \left(x + 1\right) \mathmr{and} 25 y + 150 = 3 x + 3$. or

$3 x - 25 y = 147$

The equation of line is $3 x - 25 y = 147$ [Ans]