Question

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

Answer 1

Equation of the line is `y = -15/2 x -26`

Explanation:

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

is `m_1= 2/15` [Compared with slope-intercept form of equation]

The product of slopes of the pependicular lines is `m_1*m_2=-1`

`:.m_2= -15/2`. The equation of line passing through

`(x_1,y_1)` having slope of `m_2` is `y-y_1=m_2(x-x_1)`.

The equation of line passing through `(-4,4)` having slope of

`-15/2` is `y-4=-15/2(x+4) or y = -15/2 x +4-30`. or

`y = -15/2 x -26`.

Equation of the line is `y = -15/2 x -26` [Ans]