Exercises: Drawing graphs of linear functions

Consider the function $f$ with $y = 0.3 \cdot x$ .

Compute a table of values for $f$ with $x \in [- 3,3]$ where the step length is $Δ x = 1$ .

For this task you need the following basic knowledge: Linear function
The table of values for $y = 0.3 \cdot x$ with step length $Δ x = 1$ :
x
-3
-2
-1
0
1
2
3
y
-0.9
-0.6
-0.3
0
0.3
0.6
0.9
Plot the points of the function $f$ in a coordinate system and draw the graph of the function $f$ .

For this task you need the following basic knowledge: Linear function
Points of the function $f$ in the coordinate system and graph of the function $f$ :
Zu welcher besonderen Art von Geraden gehört der Graph der Funktion $f$ ?

For this task you need the following basic knowledge: Linear function
The graph of the function $f$ is a line that passes through the origin $(0 | 0)$ of the coordinate system.
Check by calculation whether the points $P (5 | 1.4)$ and $Q (8 | 2.4)$ lie on the graph of the function $f$ .

For this task you need the following basic knowledge: Linear function
Insert the coordinates of $P$ and $Q$ into the function equation:
Point $P (5 | 1.4)$ :
$y$ $=$ $0.3 \cdot x$
↓
plug in coordinates
$1.4$ $=$ $0.3 \cdot 5$
$1.4$ $=$ $1.5$
↓
false statement
$=$
Answer: The point $P$ does not lie on the graph of the function $f$ .
Point $Q (8 | 2.4)$ :
$y$ $=$ $0.3 \cdot x$
↓
plug in coordinates
$2.4$ $=$ $0.3 \cdot 8$
$2.4$ $=$ $2.4$
↓
true statement
$=$
Answer: The point $Q$ lies on the graph of the function $f$ .
Additional illustration of the graph with the two points $P$ and $Q$
(Ths is not required by the problem setting, but just provided for better visualization.)
$P (5 | 1.4) \notin G_{f}$
$Q (8 | 2.4) \in G_{f}$

x	-3	-2	-1	0	1	2	3
y	-0.9	-0.6	-0.3	0	0.3	0.6	0.9

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$y$	$=$	$0.3 \cdot x$
	↓	plug in coordinates
$1.4$	$=$	$0.3 \cdot 5$
$1.4$	$=$	$1.5$
	↓	false statement
	$=$

$y$	$=$	$0.3 \cdot x$
	↓	plug in coordinates
$2.4$	$=$	$0.3 \cdot 8$
$2.4$	$=$	$2.4$
	↓	true statement
	$=$

Exercises: Drawing graphs of linear functions

Insert the coordinates of P and Q into the function equation:

Additional illustration of the graph with the two points P and Q

Insert the coordinates of $P$ and $Q$ into the function equation:

Additional illustration of the graph with the two points $P$ and $Q$