Final answer:
The equation of the line that passes through (-2,2) and is parallel to y = (1/5)x - 3 is y = (1/5)x + 12/5.
Step-by-step explanation:
To find the equation of the line that is parallel to y = (1/5)x - 3 and passes through the point (-2,2), we need to find the slope of the given line. The slope of a line in the form y = mx + b is equal to the coefficient of x, so in this case, the slope is 1/5.
Since we know that parallel lines have the same slope, the equation of the parallel line can be written as y = (1/5)x + b. Now we can substitute the coordinates of the given point into the equation to find the value of b. Plugging in (-2,2) gives us 2 = (1/5)(-2) + b. Solving for b, we get b = 12/5.
Therefore, the equation of the line that passes through (-2,2) and is parallel to y = (1/5)x - 3 is y = (1/5)x + 12/5, which is option D.