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[tex]3x + y = 6[/tex]
[tex]y = - 3x + 6[/tex]
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 ;
[tex]( - 3) \times (m) = - 1[/tex]
m is the slope of the line which we want.
[tex] - 3m = - 1[/tex]
Negatives simplifies
[tex]3m = 1[/tex]
Divide sides by 3
[tex] \frac{3m}{3} = \frac{1}{3} \\ [/tex]
[tex]m = \frac{1}{3} \\ [/tex]
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We have following equation to find the point-slope form of the linear functions :
[tex]y - y(0) = m(x - x(0))[/tex]
x(0) and y(0) are the coordinates of the point which the line passed through.
[tex]y - 8 = \frac{1}{3} (x - 0) \\ [/tex]
[tex]y - 8 = \frac{1}{3} x \\ [/tex]
Add sides 8
[tex]y = \frac{1}{3} x + 8 \\ [/tex]
Done....
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