Question

Write and equati9n of a l8ne that passes through (1,-2) and is perpendicular to -4x+7y=21

Answer 1

Given:

A line passes through (1,-2) and is perpendicular to
`-4x+7y=21`.

To find:

The equation of that line.

Solution:

We have, equation of perpendicular line.

`-4x+7y=21`

Slope of this line is

`m_1=-\frac{\text{Coefficient of x}}{\text{Coefficient of y}}`

`m_1=-(-4)/(7)`

`m_1=(4)/(7)`

Product of slope of two perpendicular lines is -1.

`m_1* m_2=-1`

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

`m_2=-(7)/(4)`

Now, slope of required line is
`-(7)/(4)` and it passes through (1,-2). So, the equation of line is

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

where, m is slope.

`y-(-2)=-(7)/(4)(x-1)`

`4(y+2)=-7(x-1)`

`4y+8=-7x+7`

`4y+7x=7-8`

`7x+4y=-1`

Therefore, the equation of required line is
`7x+4y=-1`.