Question

Write an equation for a line perpendicular to y=3x+1 and passing through the point (6,2)

Answer 1

`y = -(1)/(3)x + 4`

Explanation:

Required

Equation of line

passes through
`(6,2)`

In an equation of the form
`y =mx + b`; the slope is
`m`

So, by comparison;

The slope of
`y = 3x + 1` is:
`m =3`

From the question, we understand that the required equation is perpendicular to
`y = 3x + 1`

This means that its slope is:

`m_2 =-(1)/(m)`

So, we have:

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

The line equation is:

`y = m_2(x - x_1) + y_1`

Where:

`(x_1,y_1) = (6,2)`

So, we have:

`y = -(1)/(3)(x - 6) + 2`

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

`y = -(1)/(3)x + 4`