Hello!
To find the equation of a line parallel to y = 1/2x - 4, first, we need to know that if two line are parallel, then their slopes are equivalent.
Thus, we create a new equation in slope-intercept form, which includes the original slope, which is currently 1/2.
Since the equation needs a y-intercept, we would substitute the given point into the equation and solve.
y = 1/2x + b (substitute the given ordered pair)
-6 = 1/2(9) + b
-6 = 4.5 + b (subtract 4.5 to both sides)
b = -10.5
Therefore, the equation of the line parallel to y = 1/2x - 4 is y = 1/2x - 10.5. This is also written as y = 1/2x - 21/2.
