Answer:
(a) Parallel lines with same slope 3 but different y-intercepts
(b) Lines with different slopes all with same y-intercept and these four lines intersect at (0, 2), (0, 2) is also the solution to the system of these four equations
(c) New equation is outside both A and B sets; outside both ellipses A and B but inside the rectangle
Step-by-step explanation:
All equations provided are those of a straight line in slope-intercept form
y = mx + c
where
m = slope and c = y-intercept
(a) Description of lines in set A
The lines in set A are
y = 3x + 3
y = 3x - 4
y = 3x - 2
All three lines have the same slope m but different y-intercepts
So all three lines are parallel to each other
(b) The lines in set B are
y = x - 2
y = 9x - 2
y = -2x - 2
y = 3x - 2
All four lines have the same y-intercept but different slopes
Therefore all four lines will intersect at (0, -2) on a graph
This would also be the solution to the set of the four equations
(c) New equation -2x + 3
This has slope -2 and y-intercept 3 so it does not obey the properties of the lines in set A or set B.
So this equation will be outside both A and B ellipses but within the outer rectangle along with y = x + 3, y = -4x + 2 and y = 2x - 4 which are in the rectangle but outside both A and B
