# What is the equation of the line perpendicular to y=2/15x  that passes through  (-4,4) ?

May 21, 2018

Equation of the line is $y = - \frac{15}{2} x - 26$

#### Explanation:

Slope of the line,  y=2 /15 x ; [y=m x+c]

is ${m}_{1} = \frac{2}{15}$ [Compared with slope-intercept form of equation]

The product of slopes of the pependicular lines is ${m}_{1} \cdot {m}_{2} = - 1$

$\therefore {m}_{2} = - \frac{15}{2}$. The equation of line passing through

$\left({x}_{1} , {y}_{1}\right)$ having slope of ${m}_{2}$ is $y - {y}_{1} = {m}_{2} \left(x - {x}_{1}\right)$.

The equation of line passing through $\left(- 4 , 4\right)$ having slope of

$- \frac{15}{2}$ is $y - 4 = - \frac{15}{2} \left(x + 4\right) \mathmr{and} y = - \frac{15}{2} x + 4 - 30$. or

$y = - \frac{15}{2} x - 26$.

Equation of the line is $y = - \frac{15}{2} x - 26$ [Ans]