Applied exercises: Linear functions

A water supplier charges 1.50 € per $m^{3}$ of water (consumption costs).

In addition, the customer must pay a monthly basic fee of 6 € for maintenance work carried by the supplier.

Complete the table.
Water consumption(in m³)
0
1
2
3
7,8
15
20
Consumption costs (in €)
Total costs (in €)

For this task you need the following basic knowledge: Linear function
You calculate the total cost as the sum of the water consumption cost per $m^{3}$ and the basic fee. (Even if no water is consumed, the basic fee must be paid).
0 $m^{3}$ cost $0 \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = 0 \cdot 1.50 € + 6 € = 6 €$
1 $m^{3}$ costs $0 \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = 1 \cdot 1.50 € + 6 € = 7.50 €$
2 $m^{3}$ cost $0 \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = 2 \cdot 1.50 € + 6 € = 9 €$
Accordingly, you calculate the other values in the table.
The complete table looks like this:
Water consumption(in m³)
0
1
2
3
7,8
15
20
Consumption costs(in €)
0
1.50
3.00
4.50
11.70
22.50
30.00
Total costs (in €)
6.00
7.50
9.00
10.50
17.70
28.50
36.00
Draw the graph of the function $f$ describing the total monthly bill $y$ (in €) in terms of the water consumption $x$ (in $m^{3}$ ).
Also determine the equation of $f$ .

For this task you need the following basic knowledge: Linear function
Drawing the graph of $f$
From the table you can take the coordinates of 2 points, e.g. $P (0 | 6)$ and $Q (2 | 9)$ .
Draw the two points in a coordinate system and connect them with a half line starting at point $P$ .
Note: There is no negative water consumption. Therefore, the graph of the function $f$ starts at the point $P$ .
Determining of the function equation:
1 $m^{3}$ water costs $1 \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = 1 \cdot 1.50 € + 6 €$
2 $m^{3}$ cost $2 \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = 2 \cdot 1.50 € + 6 €$
........
$x$ $m^{3}$ cost $x \cdot 1.50 €$ plus the basic fee of 6 € $\Rightarrow$ Total costs: $y = x \cdot 1.50 € + 6 €$
These considerations lead you to the function equation: $y = 1.5 \cdot x + 6$
Answer: The function equation is: $y = 1.5 \cdot x + 6$

Water consumption(in m³)	0	1	2	3	7,8	15	20
Consumption costs(in €)	0	1.50	3.00	4.50	11.70	22.50	30.00
Total costs (in €)	6.00	7.50	9.00	10.50	17.70	28.50	36.00

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Applied exercises: Linear functions

Drawing the graph of f

Determining of the function equation:

Drawing the graph of $f$