Middle Years

Worksheet

1

For each of the following statements:

i

Express as an equation.

ii

State whether the equation is linear.

a

y is equal to 7 less than 2 groups of x.

b

y equals x divided by 2 plus 8.

c

y equals - 1 divided by x plus 6.

d

y plus the quotient of x and the square of - 4 is equal to 14.

2

For each of the following tables representing a linear relationship:

i

State what happens to the y-value when the x-value increases by 1.

ii

Describe the rule between x and y in words.

iii

Write the linear equation for the rule between x and y.

a

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 6 | 12 | 18 | 24 | 30 |

b

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 8 | 9 | 10 | 11 | 12 |

c

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | -7 | -8 | -9 | -10 | -11 |

d

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | -2 | -6 | -10 | -14 | -18 |

e

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 7 | 9 | 11 | 13 | 15 |

3

Consider the following table:

a

For every 1 unit increase in the x-value, is there a consistent change in the \\y-value?

b

State the change in y for every 1 unit increase in x.

x | 9 | 18 | 27 | 36 |
---|---|---|---|---|

y | -68 | -131 | -194 | -257 |

c

Explain why we can say that the relationship between x and y is linear.

d

Write the linear equation that describes the relationship between x and y.

e

Explain how the answer to part (b) helps in writing the rule for the linear relationship.

4

For each of the following tables, state whether the relationship between x and y is linear:

a

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 4 | 8 | 12 | 16 | 20 |

b

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 4 | 5 | 6 | 7 | 8 |

c

x | 1 | 2 | 4 | 7 | 8 |
---|---|---|---|---|---|

y | 5 | 8 | 11 | 14 | 17 |

d

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | -1 | 3 | 7 | 11 | 15 |

e

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 5 | 1 | -3 | -7 | -11 |

f

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 5 | 7 | 13 | 19 | 24 |

g

x | 1 | 2 | 7 | 9 | 13 |
---|---|---|---|---|---|

y | -3 | -3 | -3 | -3 | -3 |

h

x | 5 | 10 | 15 | 20 | 25 |
---|---|---|---|---|---|

y | 15 | 30 | 45 | 60 | 75 |

i

x | -1 | 0 | 1 | 2 |
---|---|---|---|---|

y | 7 | 11 | 7 | 3 |

j

x | -1 | 0 | 1 | 2 |
---|---|---|---|---|

y | 3 | 7 | 11 | 15 |

k

x | -1 | 0 | 1 | 2 |
---|---|---|---|---|

y | 3 | 3 | 3 | 3 |

l

x | -1 | 0 | 1 | 2 |
---|---|---|---|---|

y | 3 | 7 | 11 | 13 |

m

x | 3 | 3 | 3 | 3 |
---|---|---|---|---|

y | 0 | 3 | 6 | 9 |

n

x | 0 | 3 | 6 | 9 |
---|---|---|---|---|

y | -7 | 0 | 7 | 14 |

o

x | 0 | 1 | 3 | 7 |
---|---|---|---|---|

y | 14 | 7 | 0 | -7 |

p

x | -6 | -5 | -3 | 1 |
---|---|---|---|---|

y | 0 | 9 | 18 | 27 |

q

x | -6 | -3 | 0 | 6 |
---|---|---|---|---|

y | 27 | 18 | 9 | 0 |

r

x | -6 | -3 | 0 | 3 |
---|---|---|---|---|

y | 0 | 9 | 18 | 27 |

5

For each of the following tables:

i

Use the pattern to find the value of y, when x = 0.

ii

Write the linear equation that describes the relationship between x and y.

iii

Hence, complete the table.

a

x | 1 | 2 | 3 | 4 | 5 | 14 |
---|---|---|---|---|---|---|

y | 4 | 8 | 12 | 16 | 20 |

b

x | 1 | 2 | 3 | 4 | 5 | 30 |
---|---|---|---|---|---|---|

y | -1 | 1 | 3 | 5 | 7 |

c

x | -16 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

y | -2 | -4 | -6 | -8 | -10 |

d

x | -30 | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|---|

y | 52 | 44 | 36 | 28 | 20 |

e

x | 1 | 2 | 3 | 4 | 5 | 30 |
---|---|---|---|---|---|---|

y | -13 | -20 | -27 | -34 | -41 |

6

Given that the linear relationship between x and y is in the form y = m x + c, for each of the following tables:

i

Find the values of m and c.

ii

Write the linear equation that describes the relationship between x and y.

iii

Hence, complete the table.

a

x | 0 | 1 | 2 | 3 | 4 | 5 | 21 |
---|---|---|---|---|---|---|---|

y | 0 | 2 | 4 | 6 | 8 | 10 |

b

x | 0 | 1 | 2 | 3 | 4 | 5 | 29 |
---|---|---|---|---|---|---|---|

y | 8 | 13 | 18 | 23 | 28 | 33 |

c

x | 0 | 1 | 2 | 3 | 4 | 5 | 21 |
---|---|---|---|---|---|---|---|

y | -21 | -16 | -11 | -6 | -1 | 4 |

d

x | 0 | 1 | 2 | 3 | 4 | 5 | 65 |
---|---|---|---|---|---|---|---|

y | 24 | 21 | 18 | 15 | 12 | 9 |

7

Find the linear equation between x and y for each of the following tables:

a

x | -1 | 0 | 1 | 2 | 3 |
---|---|---|---|---|---|

y | 5 | 2 | -1 | -4 | -7 |

b

x | 1 | 2 | 3 | 4 | 5 |
---|---|---|---|---|---|

y | 7 | 10 | 13 | 16 | 19 |

c

x | -8 | -7 | -6 | -5 | -4 |
---|---|---|---|---|---|

y | -36 | -31 | -26 | -21 | -16 |

d

x | 3 | 4 | 5 | 6 | 7 |
---|---|---|---|---|---|

y | -12 | -17 | -22 | -27 | -32 |

8

The amount of medication M (in milligrams) in a patient’s body gradually decreases over time t (in hours) according to the equation M = 1050 - 15 t.

a

After 61 hours, how many milligrams of medication are left in the body?

b

How many hours will it take for the medication to be completely removed from the body?

9

A diver starts at the surface of the water and begins to descend below the surface at a constant rate. The table shows the depth of the diver over 5 minutes:

\text{Number of minutes passed }(x) | 0 | 1 | 2 | 3 | 4 |
---|---|---|---|---|---|

\text{Depth of diver in metres }(y) | 0 | 1.4 | 2.8 | 4.2 | 5.6 |

a

What is the increase in depth each minute?

b

Write an equation for the relationship between the number of minutes passed (x) and the depth (y) of the diver.

c

In the equation from part (b), what does the number in front of the x represent?

d

Find the depth of the diver after 6 minutes.

e

How long does the diver takes to reach 12.6 metres beneath the surface?

10

After Mae starts running, her heartbeat, in beats per minutes, increases at a constant rate.

a

Write down the missing value from the table:

\text{Number of minutes passed }(x) | 0 | 2 | 4 | 6 | 8 | 10 | 12 |
---|---|---|---|---|---|---|---|

\text{Heart rate }(y) | 49 | 55 | 61 | 67 | 73 | 79 |

b

What is Mae's resting heart rate?

c

Find the change in y for every increase of one minute.

d

Form an equation that describes the relationship between the number of minutes passed, x, and Mae’s heartbeat, y.

e

In the equation from part (d), what does the number in front of the x represent?

f

Find Mae’s heartbeat after twenty minutes.

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