Question

What is the equation of the line perpendicular to 3x+y=6 that passes through the point (0,8)​

Answer 1

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`3x + y = 6`

`y = - 3x + 6`

The coefficient of x is the slope of the line , So the slope of the above equation is -3 .

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Remember from now on ,

Product of multiplying the slopes of two lines which are perpendicular to each other , is -1 .

Thus ;

`( - 3) * (m) = - 1`

m is the slope of the line which we want.

`- 3m = - 1`

Negatives simplifies

`3m = 1`

Divide sides by 3

`(3m)/(3) = (1)/(3) \\`

`m = (1)/(3) \\`

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We have following equation to find the point-slope form of the linear functions :

`y - y(0) = m(x - x(0))`

x(0) and y(0) are the coordinates of the point which the line passed through.

`y - 8 = (1)/(3) (x - 0) \\`

`y - 8 = (1)/(3) x \\`

Add sides 8

`y = (1)/(3) x + 8 \\`

Done....

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