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Proportional relationships

Y ÷ x the same, k, y = kx · Foundations · 22 problems, easy to harder

▶ Watch the first one solved

How we do it

  1. Divide y by x
  2. Compare the answers
  3. Write the equation
  4. Check

The steps for Is it proportional: x 1, 2, 3; y 4, 8, 12. Every solution names its steps, so you always know what comes next.

Worked examples

Is it proportional: x 1, 2, 3; y 4, 8, 12 Easy

The question

Question: is this table proportional: x is 1, 2, 3, and y is 4, 8, 12?

x: 1, 2, 3; y: 4, 8, 12

Proportional means: y divided by x is always the same number.

We call that number k.

Then y = k times x.

proportional: y ÷ x is always the same
k = y ÷ x, y = kx

We write it as a table.

1 Divide y by x

For each pair we work out y divided by x.

4/1 is 4.

8/2 is 4.

12/3 is 4.

= 41 = 4, 82 = 4, 123 = 4

2 Compare the answers

The same number every time.

So it is proportional, and k = 4.

= always 4 → proportional

3 Write the equation

y = k x, with k = 4.

So the equation is y = 4x.

= y = 4x

4 Check

Let's check on a graph.

We put the points on the grid.

They lie on a straight line through (0, 0).

That is the picture of proportional.

So the answer is right!

Let's look back.

First: divide y by x.

Then: compare the answers.

Then: write the equation.

Last: check.

Answer
= y = 4x

▶ Watch it solved

Is it proportional: x 2, 3, 5; y 6, 9, 16 Medium

The question

Question: is this table proportional: x is 2, 3, 5, and y is 6, 9, 16?

x: 2, 3, 5; y: 6, 9, 16

Proportional means: y divided by x is always the same number.

We call that number k.

Then y = k times x.

proportional: y ÷ x is always the same
k = y ÷ x, y = kx

We write it as a table.

1 Divide y by x

For each pair we work out y divided by x.

6/2 is 3.

9/3 is 3.

16/5 is 3.2.

= 62 = 3, 93 = 3, 165 = 3.2

2 Compare the answers

The answers are not the same.

So it is not proportional.

= not the same → not proportional

3 Check

Let's check: the first two pairs already give different answers.

So the answer is right!

6 ÷ 2 ≠ 9 ÷ 3

Let's look back.

First: divide y by x.

Then: compare the answers.

Last: check.

Answer
= not the same → not proportional

▶ Watch it solved

4 tickets cost $28 and 6 tickets cost $42. Is the cost proportional… Harder

The question

Question: 4 tickets cost $28, and 6 cost $42: is the cost proportional to the number of tickets?

4 tickets: $28, 6 tickets: $42

Let x be the number of tickets.

Let y be the cost.

x = tickets, y = cost

Proportional means: y divided by x is always the same number.

We call that number k.

Then y = k times x.

proportional: y ÷ x is always the same
k = y ÷ x, y = kx

1 Divide y by x

For each pair we work out y divided by x.

28/4 is 7.

42/6 is 7.

= 284 = 7, 426 = 7

2 Compare the answers

The same number every time.

So it is proportional, and k = 7.

= always 7 → proportional

3 Write the equation

y = k x, with k = 7.

So the equation is y = 7x.

= y = 7x

4 Check

Let's check: k times x should give each y.

7 times 4 is 28.

7 × 4 = 28

7 times 6 is 42.

So the answer is right!

7 × 6 = 42

Let's look back.

First: divide y by x.

Then: compare the answers.

Then: write the equation.

Last: check.

Answer
= y = 7x

▶ Watch it solved

Practice

Try each one, then open the answer. Stuck? Open the problem to watch every step.

Easy

  1. is it proportional: x 1, 2, 3; y 4, 8, 12
    Answer
    = y = 4x
  2. is it proportional: x 1, 2, 3; y 3, 6, 9
    Answer
    = y = 3x
  3. is it proportional: x 2, 4, 6; y 5, 10, 15
    Answer
    = y = 2.5x
  4. is it proportional: x 1, 2, 3; y 5, 7, 9
    Answer
    Careful: the same jump each time is not enough
  5. is y = 5x proportional
    Answer
    = proportional
  6. is y = 3x + 2 proportional
    Answer
    = not proportional
  7. constant of proportionality through (2, 7)
    Answer
    = y = 3.5x
  8. constant of proportionality through (4, 12)
    Answer
    = y = 3x
  9. is it proportional: x 1, 3, 4; y 2, 6, 8
    Answer
    = y = 2x

Medium

  1. is it proportional: x 2, 3, 5; y 6, 9, 16
    Answer
    = not the same → not proportional
  2. is it proportional: x 1, 2, 4; y 2, 3, 5
    Answer
    Careful: the same jump each time is not enough
  3. is it proportional: x 2, 4, 5; y 3, 6, 7.5
    Answer
    = y = 1.5x
  4. is y = 2x - 3 proportional
    Answer
    = not proportional
  5. is y = x proportional
    Answer
    = proportional
  6. constant of proportionality through (5, 2)
    Answer
    = y = 0.4x
  7. constant of proportionality through (3, 10)
    Answer
    = y = 103x
  8. is it proportional: x 10, 20, 30, 40; y 15, 30, 45, 60
    Answer
    = y = 1.5x

Harder

  1. 4 tickets cost $28 and 6 tickets cost $42. Is the cost proportional to the number of tickets?
    Answer
    = y = 7x
  2. 3 pizzas cost $36 and 5 pizzas cost $55. Is the cost proportional to the number of pizzas?
    Answer
    Careful: the same jump each time is not enough
  3. 2 notebooks cost $5 and 6 notebooks cost $15. Is the cost proportional to the number of notebooks?
    Answer
    = y = 2.5x
  4. 5 rides cost $12 and 10 rides cost $20. Is the cost proportional to the number of rides?
    Answer
    Careful: the same jump each time is not enough
  5. is it proportional: x 1, 2, 3, 4; y 1, 4, 9, 16
    Answer
    = not the same → not proportional