Final answer:
Line a and Line c are parallel because they have the same slope of 3, while Line b is not parallel.
Step-by-step explanation:
Three lines are given:
a. Line a: y=-(1)/(3)x+1
b. Line b: y=-3x-5
c. Line c: y=3x-6
To determine which lines are parallel to each other, we need to compare their slopes. The slope of a line can be found by looking at the coefficient of x in the equation.
The slope of Line a is -(1/3), the slope of Line b is -3, and the slope of Line c is 3. Two lines are parallel if their slopes are equal.
So, Line a and Line c are parallel to each other because they have the same slope, which is 3. Line b is not parallel to either Line a or Line c since its slope is different.