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Math 8

Math 8 · Worksheets

Linear equations and graphs

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

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Linear equations and graphs

Math 8 · maddyhelps.com

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

  1. Solve x/4 − 3 = 2.

    1. a) x = 1.25
    2. b) x = 20
    3. c) x = −4
    4. d) x = 11

  2. Three friends each buy a movie ticket and a $5 popcorn. They spend $51 in all. Which equation gives the price of one ticket, t?

    1. a) 5(t + 3) = 51
    2. b) 3t + 5 = 51
    3. c) 3(t + 5) = 51
    4. d) t + 15 = 51

  3. A candle is 30 cm tall and burns down 2 cm every hour. Its table of values starts (0, 30), (1, 28), (2, 26), (3, 24). After how many hours will it be 10 cm tall?

    1. a) 10 hours
    2. b) 20 hours
    3. c) 15 hours
    4. d) 5 hours

  4. Solve 3(x + 4) = 27.

    1. a) x = 9
    2. b) x = 5
    3. c) x = 13
    4. d) x = 23

  5. Which table of values shows a linear relation?

    1. a) x: 1, 2, 4, 5 and y: 2, 4, 6, 8
    2. b) x: 1, 2, 3, 4 and y: 2, 4, 8, 16
    3. c) x: 1, 2, 3, 4 and y: 7, 4, 1, −2
    4. d) x: 1, 2, 3, 4 and y: 1, 4, 9, 16

  6. Five friends share a restaurant bill equally, and each pays $14. Which equation gives the total bill, b?

    1. a) 5b = 14
    2. b) b/5 = 14
    3. c) b − 5 = 14
    4. d) 14b = 5

  7. Solve −6x = 42.

    1. a) x = −7
    2. b) x = 7
    3. c) x = −252
    4. d) x = 48

  8. Solve x/3 = −5.

    1. a) x = −2
    2. b) x = −15
    3. c) x = −8
    4. d) x = 15

  9. Four friends split the cost of a pizza equally, and each also buys a $3 drink. Each friend spends $9 in all. How much did the pizza cost?

    1. a) $24
    2. b) $48
    3. c) $36
    4. d) $6

  10. Which point is on the graph of y = 4 − 2x?

    1. a) (−2, 3)
    2. b) (3, 6)
    3. c) (3, 2)
    4. d) (3, −2)

Answer key · Linear equations and graphs

Math 8 · maddyhelps.com

  1. b) x = 20 — Add 3 to both sides, x/4 = 5, then multiply both sides by 4: x = 20. Check: 20 ÷ 4 − 3 = 5 − 3 = 2 ✓. x = 11 multiplies the 2 by 4 but not the 3 — whatever you do to a side, you do to all of it — and x = −4 subtracts 3 instead of adding it.
  2. c) 3(t + 5) = 51 — Each friend spends t + 5, and there are three friends: 3(t + 5) = 51, so t + 5 = 17 and a ticket costs $12. 3t + 5 = 51 buys only one popcorn for the whole group, and t + 15 = 51 buys three popcorns but only one ticket.
  3. a) 10 hours — The candle has to lose 30 − 10 = 20 cm at 2 cm an hour, which takes 20 ÷ 2 = 10 hours — extend the table and you reach (10, 10). 15 hours is when it burns down completely, and 20 hours counts the centimetres it loses as if they were hours.
  4. b) x = 5 — Divide both sides by 3 first, x + 4 = 9, then subtract 4: x = 5. Check: 3(5 + 4) = 3 × 9 = 27 ✓. x = 9 stops halfway — 9 is x + 4, not x — and x = 13 adds the 4 instead of subtracting it.
  5. c) x: 1, 2, 3, 4 and y: 7, 4, 1, −2 — A relation is linear when equal steps in x give equal steps in y. In the table with y = 7, 4, 1, −2, x goes up 1 each time and y goes down 3 each time, so the points lie on a straight line — going down is fine. The table with x = 1, 2, 4, 5 looks steady because y goes up 2 each time, but x jumps from 2 to 4 once, so y rises 2 over one step and 2 over a step twice as long, and the points do not line up.
  6. b) b/5 = 14 — The bill shared among 5 people is b ÷ 5, and each share is $14: b/5 = 14, so b = $70. 5b = 14 says five whole bills come to $14, and b − 5 = 14 takes $5 off the bill instead of sharing it.
  7. a) x = −7 — Divide both sides by −6: x = 42 ÷ (−6) = −7. Check: −6 × (−7) = 42 ✓. x = 7 forgets that a positive divided by a negative is negative, and its check fails: −6 × 7 = −42.
  8. b) x = −15 — x divided by 3 gives −5, so multiply both sides by 3: x = −15. Check: −15 ÷ 3 = −5 ✓. x = 15 loses the sign, and −8 subtracts 3 instead of multiplying — a division is undone by multiplying.
  9. a) $24 — Each friend's $9 is a quarter of the pizza plus a drink: p/4 + 3 = 9. Subtract 3 to get p/4 = 6, then multiply by 4: p = 24, so the pizza cost $24. $6 is one friend's share, and $36 is everything the group spent, drinks included.
  10. d) (3, −2) — Substitute x = 3: y = 4 − 2 × 3 = 4 − 6 = −2 ✓. (3, 6) subtracts before multiplying, (4 − 2) × 3, and (3, 2) drops the sign of −2. (−2, 3) has the right numbers in the wrong order — x comes first.