Question

How to solve for "Find the equation of the line that is perpendicular to y = -2/3x and contains point (4,-8)" ?

Answer 1

`y=(3)/(2)x+(-14)`

Explanation:

Equation of a line has been given as,

`y=-(2)/(3)x` --------(1)

Slope of the line is,

`m_1=-(2)/(3)`

By the property of perpendicular lines,

If the two lines having slopes
`m_1` and
`m_2` are perpendicular to each other,
`m_1* m_2=-1`

Therefore, slope of the line perpendicular to the line (1) will be,

`-(2)/(3)* m_2=-1`

`m_2=(3)/(2)`

If this line passes through a point (4, -8) equation of the line will be,

`y-y'=m_2(x-x')`

`y+8=(3)/(2)(x-4)`

`y=(3)/(2)x-6-8`

`y=(3)/(2)x-14`