Teacher: one page per learner, printed A4. Sections A to E count toward
Written Works; see assessment.md §1. The unit has its own column
everywhere a slope is asked for — a single blank invites a bare number, and the bare
number is the error this week exists to fix. In D, two of the five zeros mean nothing;
a learner who writes a meaning on all five has not read the question. The answer key at the
foot is screen-only.
A From the equation — the unit column is not optional
Function
Slope
Its unit
Zero
y = 6x − 18 (₱ per hour)
y = 20 − 5x (litres, minutes)
y = 10 − 2.5x (kg, days)
3y = 9x + 6 (₱ per kg)
B From two points
Through
Slope
(0, 1) and (4, 9)
(0, 8) and (4, 0)
(2, 5) and (6, 5)
(3, 1) and (3, 7)
C From a table
x
0
3
6
9
slope
y
2
8
14
20
x
0
2
4
6
slope
y
30
22
14
6
x does not go up by one. Look at what it does go up by.
D Find the zero — then say what it means,
or that it means nothing
Situation
Zero
What the zero means here
A tank holds 180 litres and drains at 15 litres per minute
A tricycle charges ₱25 plus ₱10 per kilometre
A candle 24 cm tall burns 3 cm per hour
A courier charges ₱60 plus ₱25 per kilogram
A worker earns ₱80 per hour and nothing to start
E True or false?
A slope can be given without a unit.
The zero is where x = 0.
A slope of −5 is steeper than one of 4.
Every zero means something.
F In one sentence each
What is the difference between a zero and a y-intercept?
Why must a slope carry a unit?
★ The challenge
y = 12x + 30 → zero = −2.5
Check it: substitute x = −2.5 and show that y = 0.
The fare function is for a tricycle ride. What does −2.5 mean?
Change one thing in the situation so that the zero does mean something.
Write your new function and its zero.
Answer key — screen only, not printed. A · 6, pesos per hour, zero 3 · −5, litres per minute, zero 4 ·
−2.5, kilograms per day, zero 4 · 3 (divide by 3 first), pesos per kilogram,
zero −2/3 B · 2 · −2 · 0 · undefined (not 0 — B3 is the zero one) C · 2 (Δy = 6 over Δx = 3, not 6) · −4 (Δy = −8 over Δx = 2) D · 12 — the tank is empty after 12 minutes · −2.5 — nothing, you cannot travel
a negative distance · 8 — the candle is gone after 8 hours · −2.4 — nothing, a parcel
cannot have a negative mass · 0 — no hours worked, no pay (this one does mean
something) E · false · false · true · false |
F · 1. the zero is where y = 0, the y-intercept is where x = 0 · 2. a slope is a rate,
and the unit says what it is a rate of ★ · 1. 12(−2.5) + 30 = −30 + 30 = 0 ✔ · 2. nothing — a ride cannot be minus
two and a half kilometres · 3. any falling function, e.g. a ₱30 load spent at ₱12 per
kilometre, y = 30 − 12x, zero 2.5 — the load runs out after 2.5 km A row 4 is the one that catches most learners — 3y = 9x + 6 is not in y = form yet.
A learner writing 9 has read the equation, not solved it. D rows 2 and 4 are the point of the sheet. If a learner has written a meaning on all
five rows, that is the finding — not the arithmetic.