Explore · MATH-5B-C12-L05-OPEN
A line passes through (0,0) and (2,6). What is y when x=1 at a constant rate?
Great Inheritance Mathematics Term B · Original independent course
Straight Line Graphs
Watch for: Confusing rising graph with increasing speed when axes differ.. Explain what the quantities mean before calculating.
Opening task
Prerequisite check
Before instruction · MATH-5B-C12-L05-PREREQ
Complete the constant pattern (1,2), (2,4), (3, __).
Show worked answer (after attempting)
Answer: 6
Each y-coordinate is twice x.
Understand the idea
Interpret straight line graphs in meaningful grade-level contexts and distinguish patterns from extrapolation. The essential earlier idea is: Chapter 12 coordinates and unit rate as conceptual context.. The model below will always use the actual quantities from the worked problem. Check confusing rising graph with increasing speed when axes differ when you explain your answer.
Three worked examples
Worked example 1 · MATH-5B-C12-L05-Q01
A line passes through (0,0) and (2,4). What is y when x=1 at a constant rate?
Solution: 2
At a constant rate, y = 2 × x. For x=2, y=4; for x=1, y=2. This is descriptive for the given range, not unrestricted extrapolation.
Worked example 2 · MATH-5B-C12-L05-Q02
A faucet fills 3 L every minute. How much after 3 minutes?
Solution: 9 L
At a constant rate, y = 3 × x. For x=3, y=9; for x=1, y=3. This is descriptive for the given range, not unrestricted extrapolation.
Worked example 3 · MATH-5B-C12-L05-Q03
Interpret the line through points [(1, 4), (2, 8), (3, 12), (4, 16)]. State y at x=4 and its unit rate.
Solution: y=16; rate=4 per x-unit
At a constant rate, y = 4 × x. For x=4, y=16; for x=1, y=4. This is descriptive for the given range, not unrestricted extrapolation.
Check understanding
1 · MATH-5B-C12-L05-Q04
A line passes through (0,0) and (2,6). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 3
At a constant rate, y = 3 × x. For x=2, y=6; for x=1, y=3. This is descriptive for the given range, not unrestricted extrapolation.
2 · MATH-5B-C12-L05-Q05
A faucet fills 4 L every minute. How much after 3 minutes?
Show worked answer (after attempting)
Answer: 12 L
At a constant rate, y = 4 × x. For x=3, y=12; for x=1, y=4. This is descriptive for the given range, not unrestricted extrapolation.
3 · MATH-5B-C12-L05-Q06
Interpret the line through points [(1, 5), (2, 10), (3, 15), (4, 20)]. State y at x=4 and its unit rate.
Show worked answer (after attempting)
Answer: y=20; rate=5 per x-unit
At a constant rate, y = 5 × x. For x=4, y=20; for x=1, y=5. This is descriptive for the given range, not unrestricted extrapolation.
Guided practice
1 · MATH-5B-C12-L05-Q07
A line passes through (0,0) and (2,8). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 4
At a constant rate, y = 4 × x. For x=2, y=8; for x=1, y=4. This is descriptive for the given range, not unrestricted extrapolation.
2 · MATH-5B-C12-L05-Q08
A faucet fills 5 L every minute. How much after 3 minutes?
Show worked answer (after attempting)
Answer: 15 L
At a constant rate, y = 5 × x. For x=3, y=15; for x=1, y=5. This is descriptive for the given range, not unrestricted extrapolation.
3 · MATH-5B-C12-L05-Q09
Interpret the line through points [(1, 6), (2, 12), (3, 18), (4, 24)]. State y at x=4 and its unit rate.
Show worked answer (after attempting)
Answer: y=24; rate=6 per x-unit
At a constant rate, y = 6 × x. For x=4, y=24; for x=1, y=6. This is descriptive for the given range, not unrestricted extrapolation.
4 · MATH-5B-C12-L05-Q10
A line passes through (0,0) and (2,10). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 5
At a constant rate, y = 5 × x. For x=2, y=10; for x=1, y=5. This is descriptive for the given range, not unrestricted extrapolation.
Independent practice
1 · MATH-5B-C12-L05-Q11
A faucet fills 6 L every minute. How much after 3 minutes?
Show worked answer (after attempting)
Answer: 18 L
At a constant rate, y = 6 × x. For x=3, y=18; for x=1, y=6. This is descriptive for the given range, not unrestricted extrapolation.
2 · MATH-5B-C12-L05-Q12
Interpret the line through points [(1, 7), (2, 14), (3, 21), (4, 28)]. State y at x=4 and its unit rate.
Show worked answer (after attempting)
Answer: y=28; rate=7 per x-unit
At a constant rate, y = 7 × x. For x=4, y=28; for x=1, y=7. This is descriptive for the given range, not unrestricted extrapolation.
3 · MATH-5B-C12-L05-Q13
A line passes through (0,0) and (2,12). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 6
At a constant rate, y = 6 × x. For x=2, y=12; for x=1, y=6. This is descriptive for the given range, not unrestricted extrapolation.
4 · MATH-5B-C12-L05-Q14
A faucet fills 7 L every minute. How much after 3 minutes?
Show worked answer (after attempting)
Answer: 21 L
At a constant rate, y = 7 × x. For x=3, y=21; for x=1, y=7. This is descriptive for the given range, not unrestricted extrapolation.
5 · MATH-5B-C12-L05-Q15
Interpret the line through points [(1, 8), (2, 16), (3, 24), (4, 32)]. State y at x=4 and its unit rate.
Show worked answer (after attempting)
Answer: y=32; rate=8 per x-unit
At a constant rate, y = 8 × x. For x=4, y=32; for x=1, y=8. This is descriptive for the given range, not unrestricted extrapolation.
6 · MATH-5B-C12-L05-Q16
A line passes through (0,0) and (2,14). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 7
At a constant rate, y = 7 × x. For x=2, y=14; for x=1, y=7. This is descriptive for the given range, not unrestricted extrapolation.
7 · MATH-5B-C12-L05-Q17
A faucet fills 8 L every minute. How much after 3 minutes?
Show worked answer (after attempting)
Answer: 24 L
At a constant rate, y = 8 × x. For x=3, y=24; for x=1, y=8. This is descriptive for the given range, not unrestricted extrapolation.
8 · MATH-5B-C12-L05-Q18
Interpret the line through points [(1, 9), (2, 18), (3, 27), (4, 36)]. State y at x=4 and its unit rate.
Show worked answer (after attempting)
Answer: y=36; rate=9 per x-unit
At a constant rate, y = 9 × x. For x=4, y=36; for x=1, y=9. This is descriptive for the given range, not unrestricted extrapolation.
Challenge and error analysis
1 · MATH-5B-C12-L05-ERR1
The assigned question is: “A faucet fills 11 L every minute. How much after 3 minutes?” A learner wrote: “I treated the constant rate of change in the data containing 11 as an extra starting amount; I concluded 33.1 L.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: 33 L
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: 33 L. Recompute from the given data: At a constant rate, y = 11 × x. For x=3, y=33; for x=1, y=11. This is descriptive for the given range, not unrestricted extrapolation.
2 · MATH-5B-C12-L05-ERR2
The assigned question is: “Interpret the line through points [(1, 12), (2, 24), (3, 36), (4, 48)]. State y at x=4 and its unit rate.” A learner wrote: “I treated the constant rate of change in the data containing 1 as an extra starting amount; I concluded y=49; rate=12 per x-unit.” Identify a concrete invalid step or assumption. Work out the correct result and explain why it is valid.
Show worked answer (after attempting)
Answer: Correct result: y=48; rate=12 per x-unit
The attempted reasoning or reported result does not satisfy the specified operation, units or geometric conditions. Correct mathematical result: y=48; rate=12 per x-unit. Recompute from the given data: At a constant rate, y = 12 × x. For x=4, y=48; for x=1, y=12. This is descriptive for the given range, not unrestricted extrapolation.
Exit check
Exit · MATH-5B-C12-L05-Q19
A line passes through (0,0) and (2,16). What is y when x=1 at a constant rate?
Show worked answer (after attempting)
Answer: 8
At a constant rate, y = 8 × x. For x=2, y=16; for x=1, y=8. This is descriptive for the given range, not unrestricted extrapolation.