#### Different kinds of graphs.

1.
The diagrams below show the graphs of variables a and b. Variable a is plotted on the
horisontal axis, the x-axis, and b on the vertical axis, the y-axis.
What is the relationship between a and b? Give reasons. Use the expressions directly
proportional, inversely proportional or unknown to describe the relationship between a and b.
1.1
1.2
1.3   1.4
1.5
1.6   1.7
1.8
1.9   1.10
1.11
1.12   2.
The table below shows the cost to manufacture n articles:
 Number of articles, n 1 2 5 6 8 Cost 4 8 20 24 32
2.1
Will the cost to manufacture n articles be directly proportional to n, the number of articles?
Explain.
2.2
What shape will the graph have if number of articles is plotted on the x-axis and cost
2.3
Draw the graph of number of articles on the x-axis and cost on the y-axis.
2.4
Does the graph have the shape which you predicted in 2.2?
2.5
Read from the graph the following values and clearly mark the point where you took the reading
with the letter in brackets:
2.5.1
cost to manufacture 4 articles (P).
2.5.2
the number of articles that can be manufactured if the cost is R26. (Q)
2.6
3.
The table below shows the number of hours that a number of men must work to complete a task:
 Number of men 1 2 3 6 16 24 48 Number of hours 48 24 16 8 3 2 1
3.1
Is the number of hours directly proportional to the number of men? Explain.
3.2
What shape will the graph of the data above have if number of men is plotted on the x-axis and
number of hours is plotted on the y-axis? Explain.
3.3
Draw the graph with number of men on the x-axis and the number of hours on the y-axis.
3.4
Does the graph have the predicted shape?
3.5
Read the requested values from the graph and clearly mark the point where you made the reading.
3.5.1
How many hours must 5 men work to complete the task? Is it a suitable answer? Explain.
3.5.2
How many men must work for 20 hours to complete the task? Is it a suitable answer? Explain.
3.6
What is the greatest number of hours needed to complete the task if everybody works at the
same rate? Explain.
3.7
Can the work be completed in 15 minutes? How many men will be needed? Is it a suitable
4.
In an experiment a student obtains the following values:
 a 0 1 2 3 4 8 b 0 3 6,05 7,9 12,5 23,9
4.1
Can the student claim that b is directly propotional to a? Explain.
4.2
Write down the relationship between a and b in words and in symbols.
4.3
What shape will the graph of a, on the x-axis, and b, on the y-axis, have? Explain.
4.4
Draw the graph of a, on the x-axis, and b, on the y-axis.
4.5
Read from the graph the following values and mark the point where you take the reading with the
letter in brackets:
4.5.1
the value of b if a = 6 (P)
4.5.2
the value of a if b = 10,5 (Q)
4.6
Use the formula that you wrote down in 4.2 to calculate the values of a and b in 4.5.1 and 4.5.2
How do the calculated values correspond with the values read from the graph?
5.
The table below contains values for a and b.
 a 1 4 8 16 b 16 4 2 1
5.1
5.2
Describe the relationship between a and b in words and in symbols.
5.3
What shape will the graph of a against b have? Motivate your answer.
5.4
Draw the graph of a, on the x-axis, and b, on the y-axis.
5.5
Read from the graph the following values and mark the point where you take the reading with the
letter in brackets:
5.5.1
the value of b if a = 8 (P)
5.5.2
the value of a if b = 10 (Q)
5.6
Use the formula that you wrote down in 5.2 to calculate the values of a and b in 5.5.1 and 5.5.2
How do the calculated values correspond with the values read from the graph?
6.
Values for a and b are given in the table below.
 a 0 1 2 4 b 0 1 4 16
6.1
6.2
Describe the relationship between a and b in words and in symbols.
6.3
What will the shape of the graph of a against b be? Motivate your answer.
6.4
Draw the graph of a, on the x-axis, and b, on the y-axis.
6.5
Read from the graph the following values and mark the point where you take the reading with the
letter in brackets:
6.5.1
the value of b if a = 1,5 (Q)
6.5.2
the value of a if b = 9 (P)
6.6
Use the formula that you wrote down in 6.2 to calculate the values of a and b in 6.5.1 and 6.5.2
How do the calculated values correspond with the values read from the graph?
7.
A farmer wants to make a coop with an area of 36 m². Please help the farmer.
7.1
Write down the relationship between the length and breadth of the coop in words and in symbols.
7.2
What shape will the graph of length, on the x-axis, and breadth, on the y-axis, have? Explain.
7.3
Draw up a table containing suitable possible values for the length and breadth of the coop.
7.4
Draw the graph, f, of length on the x-axis and breadth on the y-axis.
7.5
Read the following measurements from the graph and clearly mark the point where you take
the reading with the letter in brackets:
7.5.1
the breadth if the length is 3 m (P).
7.5.2
the length if the breadth is 20 m. (Q)
7.6
Draw the line g: y = x and let f and g intersect at R. Write down the co-ordinates of R.
7.7
What is special about point R?
7.8
The farmer wants the coop to be a square. Read from the graph the length of the sides of the square
and mark the point where the readings are taken.
7.9
What length of wire netting will be necessary to fence in the coop?
7.10
The farmer has 24,4 m of wire netting to use. What will the measurements of the coop be?