Inequalities & Graphing
XY Coordinate System & Plotting Points
The coordinate plane has a horizontal x-axis and vertical y-axis. Points are written as (x, y) — x tells you how far left/right, y tells you how far up/down.
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Worked Examples
Follow along with these step-by-step examples. Take your time — there's no rush!
Problem
Plot the point (3, −2)
Step-by-Step Solution
Start at the origin (0, 0).
Move 3 units to the right (positive x).
Move 2 units down (negative y).
This point is in Quadrant IV.
Answer
3 right, 2 down — Quadrant IV
Problem
What quadrant is (−4, 5) in?
Step-by-Step Solution
x = −4 is negative → left side
y = 5 is positive → upper side
Left and up = Quadrant II
Answer
Quadrant II
Problem
What are the coordinates of a point 2 left and 6 up from the origin?
Step-by-Step Solution
2 left means x = −2
6 up means y = 6
Point: (−2, 6)
Answer
(−2, 6)
Problem
A point is at (0, −5). Which axis does it lie on?
Step-by-Step Solution
x = 0 means the point is on the y-axis.
y = −5 means it is 5 units below the origin.
Answer
On the y-axis
Problem
What quadrant is (−6, −2) in?
Step-by-Step Solution
x = −6 is negative → left side.
y = −2 is negative → lower side.
Left and down = Quadrant III.
Answer
Quadrant III
Your Turn — Practice Problems
Try all 5 problems on your own first. Write out your work — that's how it sticks!
💡 Tip: Don't peek at the answers until you've genuinely tried each one.
What quadrant is (5, 3) in?
What quadrant is (−2, −7) in?
Plot (0, 4) — where does it lie?
What quadrant is (6, −1) in?
A point is at (−3, 0). Where is it?
What quadrant is (−8, 5) in?
Name the coordinates of the origin
A point is 4 right and 3 down from the origin. What are its coordinates?
What quadrant has negative x and positive y?
What quadrant has positive x and negative y?
A point is at (7, 0). Which axis does it lie on?
What are the coordinates of a point 5 left and 2 down from the origin?
Finished all 12? Give yourself a pat on the back — then check your work!
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