Exercises: Linear functions and line equations

Draw the following straight lines and give the function term.

$G_{f}$ has the slope $\frac{3}{4}$ and intersects the $y$ -axis at $- 2$ .

For this task you need the following basic knowledge: Linear function
Setting up the function term
$m = \frac{3}{4}; t = - 2$
Plug $m$ and $t$ into the general line equation $y = m x + t$ .
$\Rightarrow y = \frac{3}{4} x - 2$
Drawing the line
Select any point on the line, e.g. the $y$ -axis interception point $(0 | - 2)$ . From there go 1 to the right and according to the slope $m = \frac{3}{4}$ upwards (alternatively, also the quadruple length to avoid fractions: 4 to the right and 3 upwards). Connect the two points to form a straight line.
$G_{f}$ has the slope $0$ and intersects the $y$ -axis at $3$ .

For this task you need the following basic knowledge: Linear function
Setting up the function term
$m = 0; t = 3$
Plug $m$ and $t$ into the general line equation $y = m x + t$ .
$\Rightarrow y = 3$
Drawing the line
The line runs through the $y$ -axis intercept $(0 | 3)$ parallel to the $x$ -axis because the line has a slope of 0.
$G_{f}$ passes through the point $P (- 4 | 2)$ and is parallel to the $ x$ -axis.

For this task you need the following basic knowledge: Linear function
Setting up the function term
Since the line is parallel to the $x$ -axis, so its slope is $0 \Rightarrow m = 0$ .
The line goes through the point $(- 3 | - 2)$ . Since the slope is 0, the line has the $y$ -value $- 2$ at $x = 0$ .
Its $y$ -axis intercept is therefore $- 2$
$m = 0; t = - 2$
Plug $m$ and $t$ into the general line equation $y = m x + t$ .
$y = - 2$
Drawing the line
The line runs through the $y$ -axis interception point $(0 | - 2)$ and is parallel to the x-axis.
$G_{f}$ passes through the point $P (- 4 | 2)$ and is parallel to the $y$ -axis.

For this task you need the following basic knowledge: Linear function
Setting up the function term
This straight line cannot be described by a function equation. The gradient would be infinitely large.

However, we can still draw the straight line.
Drawing the line
The line runs through the point $(- 4 | 2)$ and is parallel to the $y$ -axis.