# Linear Review 2.docx

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```					                                                                  Grade 9 Math
Linear Review 2
____   1. Complete the table of values.

x       2         4        6         8

y

____   2. Create a table of values that represents the equation                      ?

____   3. Which line represents the equation                         ?
y
6

4

Q                      R
2

–6       –4     –2       0         2        4   6   x
–2
S                      P

–4

–6

4. This pattern of unit squares continues.
Determine an equation that relates the number of unit squares, n, to the figure number, f.

Figure 1                    Figure 2               Figure 3

5. The pattern in this table continues. Write an equation that relates the term value to the term number.

Term Number, t                        1            2           3      4        5
Term Value, w                         5            8           11     14       17

6. The first term value, f, in a pattern is 25. As the term number increases by 1, the term value increases by 4.
a) Create a table of values for the pattern.
b) Write an expression for the term value in terms of the term number, n.
7.            a) Which table of values represents a linear relation?

i)
x         1         2        3        4
y         12        0        –4       –6
ii)
x         1         2        3        4
y         11        7        3        –1
iii)
x         1         2        3        4
y         13        10       5        –2

b) Write an equation that represents the linear relation.

8. a) Create a table of values for the linear relation                    . Use –4, –2, 0, 2, 4 for values of x.

x        –4        –2        0        2        4
y
.
9. Create a table of values for the linear relation                         , then graph the relation.
Use values of x from 0 to 6.

x         0      1          2               3        4        5          6
y

y
20
18
16
14
12
10
8
6
4
2

–12 –10 –8 –6 –4 –2 0           2   4       6   8 10 12       x
–2
–4
–6
–8
–10
–12
–14
–16
–18
–20

10. Dorina is having a party. She estimates that she will need 5 sandwiches for each guest, and 12 extra
sandwiches for unexpected guests.
a) Write an equation that relates the total number of sandwiches, T, to the number of guests, p.
b) How many sandwiches will Dorina need for 16 guests?

11. A helicopter is at a height of 1600 m when it starts descending to land.
The helicopter’s height changes at an average rate of 140 m/min.
a) Write an equation that relates the height of the helicopter, H metres, to the time since the helicopter began
its descent, t minutes.
b) What is the height of the helicopter 9 min after it began its descent?

12. This is a partially completed table of values for a linear relation.
a) Determine the missing values of y.
x             1               3               5                   7   9
y             6               17

b) Write an equation that represents the linear relation.

13. Graph the following lines on the same grid. Label the lines.
i)
ii)

y

10

8

6

4

2

–6     –4       –2           0           2       4           6       x
–2

–4

14. Graph these equations on the same grid. What shape is formed by the lines?
i)
ii)
iii)
iv)

y

6

4

2

–6       –4   –2        0          2       4           6       x
–2

–4

–6
18. a) Graph the straight line that passes through the points (0, 10), (3, 7), and (10, 0).
y

10

8

6

4

2

0            2        4       6          8     10      x

b) Write an equation to describe the line.

19. Match each equation with a graph on the grid below.
i)
ii)
iii)
iv)

y
6

Graph P
4

2                  Graph Q

–6        –4       –2       0          2       4     6       x
–2                     Graph R

–4
Graph S

–6
20. Match each equation with a graph on the grid below.
i)
ii)
iii)
y
6

B
ph
Gra
4

C
A
ph

ph
Gra

Gra
2

–6       –4           –2           0                2             4             6       x
–2

–4

–6

21. Which graph on this grid has the equation y = 2x + 2?
y
8

6

4                                     hB
ap
Gr
2

–6        –4       –2           0               2              4            6        x
–2
A

Gra
ph

ph
Gra

–4
C

–6

–8

22. Match each equations with its graph below.
i)            ii)               iii)                                                               iv)
y

10

8
Graph B

6
Graph A

4
Gr

2
C
ap

ph
Gra
hD

0            2            4               6              8            10               x
23. This graph represents a linear relation.
Determine the value of x when y = 14.

y
10

8

6

4

2

0       2   4    6     8         x

24. This graph shows the relationship between the perimeter of a square and its side length.
a) Determine the perimeter of a square with side length 7.5 cm.
b) Determine the side length of a square with perimeter 46 cm.

Measurements of a Square
56

48

40
Perimeter (cm)

32

24

16

8

0       2   4    6     8    10       12   14   16   18   20
Side Length (cm)
25.    This graph shows the depth of water in a tank, in metres, as the water drains out.
a) Estimate the depth of water after 3 h.
b) Estimate how much time has passed if there is 8.5 m of water in the tank.
Draining Time
12

10
Depth (m)

8

6

4

2

0      2     4    6      8    10
Time (h)

Problem

26. This pattern of squares continues.

Figure 1 Figure 2    Figure 3        Figure 4

a) Which equation relates the number of squares, s, to the figure number, n?
i)
ii)

iii)
b) Determine the number of squares in figure 35.

27. a) Graph the following lines on the same grid. What shape do they form?
i)
ii)
iii)
iv)
y
4

2

–4    –2    0         2        4   6   8       x
–2

–4

b) When Joan graphed the lines she made a mistake. Instead of graphing           and   , she
graphed          and          .
What did Joan’s graph look like?

y
4

2

–4    –2    0         2        4   6   8       x
–2

–4

28. The sum of two rational numbers, p and q, is 1.5.
a) Make a table to show 5 possible pairs of numbers that satisfy this relation.
Include p = 1.5 and q = 1.5 in your table.

p
q

b) Graph the data. Describe your graph.

q

4

2

–4    –3     –2       –1    0       1   2   3       4 p
–2

–4

c) Write an equation for the relation.
29. Two points on the graph below have coordinates A(2,–3) and B(–4,0).
Which equation matches the graph? Show your work.
i)
ii)
iii)
y
6

4

2
B

–6   –4   –2    0        2         4       6   x
–2
A

–4

–6

30. This graph represents a linear relation.
a) Estimate the value of y when x = 9. Did you use interpolation or extrapolation to find the answer?
Explain.
b) Estimate the value of x when y = –3. Did you use interpolation or extrapolation to find the answer?
Explain.
y
8

6

4

2

–10   –8   –6    –4       –2    0           2       4   6   8   10   x
–2

–4

–6

–8

```
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