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Maths · Grade 6 · Set C
Starting Amounts and Steady Change
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C
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Goal: 15 min
Score/ 12
Remember: In y = (steady change) × x + (start), the number added on is the start and the number beside x is the change each step.

Tables, graphs and equations

1
Kai mows lawns. In the table, h is his hours and p is his dollars. How many dollars after 3 hours?
2
What equation gives p from h?
p = 3h + 4p = 4h + 3p = 7h
3
Kai's dollars are p = 3h + 4. After how many hours does he have 25 dollars?
4
In p = 3h + 4, what does the 4 tell us?
Kai earns 4 dollars each hour.Kai starts with 4 dollars.Kai works 4 hours.
5
Dee's savings are s = 2w + 1. Across is weeks w and up is dollars s. Which graph matches?
Graph 1
Graph 2
Graph 3
6
In d = 3t + 4, the graph starts at 4 on the up line when t = 0.
TrueFalse

Compare and explain

7
The equations y = 5x and y = x + 5 give the same y for every x.
TrueFalse
8
A taxi costs c dollars for m miles. Join each story to its equation.
  1. 13 dollars to start and 2 more for each mile
  2. 22 dollars for each mile and nothing to start
  3. 33 dollars for each mile
  4. 42 dollars to start and 3 more for each mile
  • Ac = 3m + 2
  • Bc = 2m + 3
  • Cc = 3m
  • Dc = 2m
9
A taxi's cost is c = 3m + 2, with m in miles. How many dollars for 5 miles?
10
Plant A grows h = 2d and plant B grows h = d + 3, with d days and h centimeters. After 4 days, which plant is taller?
Plant A is taller.Plant B is taller.They are the same height.
11
Plant A grows h = 2d and plant B grows h = d + 3, with d days and h centimeters. After how many days are the two plants the same height?
12
In y = 3x + 2, when x doubles from 1 to 2, y doubles from 5 to 10.
TrueFalse
13
Write a story that fits y = 4x + 5. Say what x and y stand for.
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Answer key · Set C
Starting Amounts and Steady Change
113 He starts with 4 and each hour adds 3: 4, 7, 10, 13.
2p = 3h + 4 At 0 hours he has 4, and each hour adds 3.
37 25 − 4 = 21, and 21 ÷ 3 = 7. Check: 3 × 7 + 4 = 25.
4Kai starts with 4 dollars. The 4 is added on whatever the hours are. It is what he has at 0 hours.
5Graph 2 At w = 0 she has 1, then 3, 5 and 7. Graph 1 starts at 2, and Graph 3 is s = 2w.
6True When t = 0, d = 3 × 0 + 4 = 4.
7False They match only for some x. For x = 2, 5x is 10 but x + 5 is 7.
81-B, 2-D, 3-C, 4-A The number beside m is the cost for each mile. The number added on is the start fee.
917 3 × 5 = 15, and 15 + 2 = 17.
10Plant A is taller. Plant A is 2 × 4 = 8 cm and plant B is 4 + 3 = 7 cm.
113 The lines cross at (3, 6). Check: 2 × 3 = 6 and 3 + 3 = 6.
12False When x = 2, y = 3 × 2 + 2 = 8, not 10. The starting amount of 2 keeps y from doubling.
13Your own words: a grown-up reads it.
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