Answer:
D) y = -1/3 x+6
Explanation:
If we want to find a line parallel to 3x+9y=7, the slopes will have to be the same because parallel lines have the same slope. Knowing y= mx+b we need to find the slope of the old line.
3x+9y=7
Subtract 3x from each side
3x-3x +9y = -3x+7
9y = -3x+7
Divide each side by 9
9y/9 = -3x/9 + 7/9
y = -1/3 x + 7/9
We know the slope of the old line is -1/3, so the slope of the parallel line is -1/3.
If we know the slope of the line and a point, we can use the point slope form of a line
y-y1 = m(x-x1)
y-4 = -1/3(x-6)
Distribute the -1/3
y-4 = -1/3 x -1/3*-6
y-4 = -1/3x +2
Add 4 to each side
y-4+4 = -1/3x +2+4
y = -1/3x+6