Final answer:
The equation of the line passing through (-4,4) parallel to y = -1/2x + 5 is y = -1/2x + 2.
Step-by-step explanation:
To find the equation of a line parallel to another line, we need to use the fact that parallel lines have the same slope. First, let's find the slope of the given line. The slope of the line y = -1/2x + 5 is -1/2. Therefore, the slope of the parallel line will also be -1/2.
Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we can substitute the slope and the coordinates of the given point into the equation to find the y-intercept. For the line passing through (-4,4), we get 4 = -1/2(-4) + b. Solving for b, we find b = 2.
Therefore, the equation of the line passing through (-4,4) parallel to y = -1/2x + 5 is y = -1/2x + 2.