SOLUTION: Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y = mx+b. (2,9); x +3y = 4 The equation of the line is

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1 x + 3 y = 4
Find the slope of this line
make y the subject
3 y = -1 x + 4
Divide by 3
y = - 1/ 3 x + 4/3
Compare this equation with y=mx+b
slope m = - 1/ 3
The slope of a line parallel to the above line will be the same
The slope of the required line will be - 1/ 3
m= - 1/ 3 ,point ( 2 , 9 )
Find b by plugging the values of m & the point in
y=mx+b
9 = - 2/ 3 + b
b= 29/3
m= - 1/3
Plug value of the slope and b in y = mx +b
The required equation isy = - 1/3 x + 29/3

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