Question

Write an equation of the line containing the given point and perpendicular to the given line. ?(0?,2?); 9x+2y=3

Answer 1

The required equation is
`y=(2)/(9)x+2`.

Explanation:

The equation of the given line is

`9x+2y=3`

If a line is defined as
`ax+by=c`, then slope of the line is

`m=(-a)/(b)`

In the given equation a=9 and b=2. Slope of the line is

`m_1=(-9)/(2)`

Product of slopes of two perpendicular line is -1.

Let the slope of required line be
`m_2`.

`m_1* m_2=-1`

`(-9)/(2)* m_2=-1`

`m_2=(2)/(9)`

Slope of required line is
`(2)/(9)` and it passes through the point (0,2). It means the y-intercept of the line is 2.

The slope intercept form of a line is

`y=mx+b`

where, m is slope and b is y-intercept.

Substitute m=2/9 and b=2 in the above equation.

`y=(2)/(9)x+2`

Therefore the required equation is
`y=(2)/(9)x+2`.