Question

Find the equation of a line that is perpendicular to Y =1/ 4x + 6 and contains the point (-2,0)

Answer 1

The equation of perpendicular line is
`y=-4x-8`.

Explanation:

The equation of given line is

`y=(1)/(4)x+6` ..... (1)

The slope intercept form of a line is

`y=mx+b` .... (2)

Where, m is slope and the y-intercept is b.

On comparing (1) and (2) we get the slope of line is
`(1)/(4)` and the y-intercept is 6.

The product of slopes of two perpendicular line is -1.

`m_1* m_2=-1`

`(1)/(4)* m_2=-1`

`m_2=-4`

The slope of perpendicular line is -4. It is given that the perpendicular line passing through the point (-2,0).

Using point slope form we get

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

`y-0=-4(x-(-2))`

`y=-4x-8`

Therefore the equation of perpendicular line is
`y=-4x-8`.