Origin — Grade 7 Accelerated, what it means and where it is taught
The point (0, 0), which every proportional graph passes through.
Taught in Grade 7 Accelerated.
Where it is taught
What it rests on
Work through these first if this one does not settle.
- Proportional — Two quantities with a constant ratio: yx = k always.
What uses it later
This idea is needed for:
- Linear but not proportional — A straight line that misses the origin, like y = 3x + 5.
Practise this idea
6 questions in the course bank use Origin, in Proportional Relationships, The Coordinate Plane.
Problem 1
Every proportional graph must pass through which point?
- (1, 1)
- (0, 0)
- (1, 0)
- (0, 1)
Worked answer
(0, 0)
Zero of one means zero of the other, so the line goes through the origin (0, 0).
Problem 2
Which relationship is NOT proportional?
- 8 apples for $4; 12 apples for $6
- A car travelling 50 miles every hour
- A gym charging $25 to join plus $15 a month
- 3 cups of flour per dozen cookies
Worked answer
A gym charging $25 to join plus $15 a month
With the gym, zero months still costs $25, so the graph misses (0,0).
It is linear (y = 15x + 25) but not proportional.
Problem 3
A table shows x = 2, 4, 7 with y = 7, 14, 24. Is it proportional?
- Yes, with k = 3.5
- No — the last pair breaks the pattern
- No — it does not pass through the origin
Worked answer
No — the last pair breaks the pattern
72 = 3.5 and 144 = 3.5 — so far so good
But 247 ≈ 3.43, which does not match
One disagreeing row is enough to rule it out.
Problem 4
A point is 5 right and 2 down from the origin. Write it as an ordered pair.
Worked answer
(5,-2)
A
c
r
o
s
s
f
i
r
s
t
.
Problem 5
A point is 3 left and 4 up from the origin. Write it as an ordered pair.
Worked answer
(-3,4)
L
e
f
t
i
s
n
e
g
a
t
i
v
e
.
Problem 6
Give the coordinates of the origin.
Worked answer
(0,0)
W
h
e
r
e
t
h
e
a
x
e
s
c
r
o
s
s
.