Final answer:
The equation of a line parallel to line m with slope -1/3 is y = (-1/3)x + b, where b is the y-intercept which varies depending on the specific line.
Step-by-step explanation:
To find the equation of a line parallel to line m that passes through the points (2,2) and (-4,4), we need to identify the slope of line m. The slope can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points the line passes through.
For our points (2,2) and (-4,4), the slope is:
m = (4 - 2) / (-4 - 2) = 2 / -6 = -1/3
A line parallel to line m will have the same slope, -1/3. To find the equation of a parallel line, we can choose any point through which the new line will pass and use the formula y = mx + b. The y-intercept (b) can vary, so let's say the new line passes through the point (x, y). The equation of the new line is then:
y = (-1/3)x + b
The exact equation will depend on the y-intercept of the line in question.