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Math 9

Math 9 · Worksheets

Linear relations

Ten questions of mixed difficulty, covering Linear relations. Print it, or work through it on screen — the answer key starts on its own page.

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Linear relations

Math 9 · maddyhelps.com

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Circle the best answer for each question. Show your work in the space provided.

  1. Figure 1 of a tile pattern has 7 tiles, figure 2 has 11 and figure 3 has 15. How many tiles are in figure 20?

    1. a) 80
    2. b) 83
    3. c) 140
    4. d) 87

  2. The graph of y = 3 is

    1. a) a vertical line through (3, 0)
    2. b) a horizontal line through (3, 0)
    3. c) a line through (0, 0) and (1, 3)
    4. d) a horizontal line through (0, 3)

  3. In a linear pattern, figure 4 has 19 squares and figure 7 has 31 squares. Which equation gives the number of squares, s, in figure n?

    1. a) s = 4n + 3
    2. b) s = 3n + 7
    3. c) s = 12n − 29
    4. d) s = 4n + 15

  4. A gym charges a $40 sign-up fee plus $15 a month. Which equation gives the total cost, C, in dollars, after m months?

    1. a) C = 15m + 40
    2. b) C = 40m + 15
    3. c) C = 55m
    4. d) C = 15(m + 40)

  5. A candle is 30 cm tall and burns down 2 cm each hour, so its height after t hours is h = 30 − 2t. After how many hours will it be 12 cm tall?

    1. a) 6 h
    2. b) 15 h
    3. c) 21 h
    4. d) 9 h

  6. Figure 1 of a pattern uses 5 toothpicks, figure 2 uses 8 and figure 3 uses 11. Which equation gives the number of toothpicks, t, in figure n?

    1. a) t = n + 3
    2. b) t = 3n + 5
    3. c) t = 3n + 2
    4. d) t = 5n

  7. A vertical line passes through the point (−2, 5). What is its equation?

    1. a) y = 5
    2. b) y = −2
    3. c) x = −2
    4. d) x = 5

  8. Which point lies on the graph of y = 2x − 3?

    1. a) (2, 7)
    2. b) (5, 4)
    3. c) (4, 5)
    4. d) (0, 3)

  9. A puppy's mass was 5 kg at 2 months, 9 kg at 4 months and 13 kg at 6 months, rising at a steady rate. If the pattern continues, what will its mass be at 9 months?

    1. a) 18 kg
    2. b) 19 kg
    3. c) 19.5 kg
    4. d) 17 kg

  10. A sunflower was 5 cm tall and grew 3 cm a day for 20 days. Using h = 5 + 3d, Jordan predicts it will be 1100 cm tall after 365 days. Why is this prediction unreliable?

    1. a) It uses interpolation, which only works for values inside the data.
    2. b) The equation gives a different height for 365 days.
    3. c) The equation should be h = 3d, since the 5 cm was not growth.
    4. d) It extrapolates far past the data, and the growth rate will not stay the same.

Answer key · Linear relations

Math 9 · maddyhelps.com

  1. b) 83 — The pattern goes up 4 each time, and figure 1 is 4 + 3, so t = 4n + 3 and figure 20 has 4(20) + 3 = 83 tiles. Multiplying figure 1 by 20 gives 140, which assumes the pattern is proportional — it is not, because of the 3 extra tiles.
  2. d) a horizontal line through (0, 3) — y = 3 says every point has a y-coordinate of 3, whatever x is, so the points form a horizontal line crossing the y-axis at 3. The vertical line through (3, 0) is x = 3, and the line through (0, 0) and (1, 3) is y = 3x.
  3. a) s = 4n + 3 — From figure 4 to figure 7 is 3 steps and 31 − 19 = 12 squares, so the pattern goes up 12 ÷ 3 = 4 each time; then 19 − 4(4) = 3, so s = 4n + 3. The equations s = 3n + 7 and s = 12n − 29 both fit figure 4 but not figure 7 — test an equation on both figures.
  4. a) C = 15m + 40 — The $15 is paid every month, so it multiplies m; the $40 is paid once, so it is the constant. Swapping them gives C = 40m + 15, and C = 55m charges the sign-up fee every month.
  5. d) 9 h — Set 30 − 2t = 12. Then 2t = 18 and t = 9 hours; check: 30 − 2(9) = 12 ✓. 15 h is when the candle burns out completely, and 6 h is 12 ÷ 2, which ignores the starting height.
  6. c) t = 3n + 2 — The count goes up 3 each time, so the equation has 3n; for figure 1, 3(1) = 3, and 2 more makes 5, so t = 3n + 2. Using the first figure's 5 as the constant gives 3n + 5, which is 8 for figure 1 — check an equation against the table before trusting it.
  7. c) x = −2 — Every point on a vertical line has the same x-coordinate, so the line is x = −2. The equation y = 5 is the horizontal line through the same point; mixing up which letter goes with which direction is the usual slip.
  8. c) (4, 5) — Substitute the x-coordinate and check the y: 2(4) − 3 = 5 ✓. The point (5, 4) swaps the coordinates — x always comes first — and (0, 3) drops the negative sign on the constant.
  9. b) 19 kg — The mass rises 4 kg every 2 months, which is 2 kg a month, so m = 2t + 1 and at 9 months m = 2(9) + 1 = 19 kg. Adding another 4 kg treats 9 months as the next entry in the table, but the table goes up 2 months at a time, not 3.
  10. d) It extrapolates far past the data, and the growth rate will not stay the same. — Day 365 is far outside the 20 days that were measured, and a sunflower stops growing long before a year is out. The arithmetic is right — 5 + 3(365) = 1100 — and that is the point: a correct calculation from a pattern that has stopped holding is still a wrong prediction.