A. $y=\frac{2}{3} x-4$
B. $y=\frac{2}{3} x+6$
C. $y=\frac{3}{2} x-4$
D. $y=-4 x+\frac{2}{3}$

Answer

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Answer

$\boxed{y = \frac{2}{3}x + 6}$

Steps

Step 1 ：Find the slope of the given line: $m = \frac{2}{3}$

Step 2 ：Since parallel lines have the same slope, use the slope and the point (0, 6) to find the equation of the new line: $y = \frac{2}{3}x + b$

Step 3 ：Plug in the point (0, 6) to find the y-intercept: $6 = \frac{2}{3}(0) + b$

Step 4 ：Solve for b: $b = 6$

Step 5 ：Write the equation of the line: $y = \frac{2}{3}x + 6$

Step 6 ：$\boxed{y = \frac{2}{3}x + 6}$