Exercises: Linear functions and line equations

Draw the following lines and determine 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
Seting up the function term
$m = \frac{3}{4}; t = - 2$
Insert $m$ and $t$ into the general line equation $y = m x + t$ .
$\Rightarrow y = \frac{3}{4} x - 2$
Draw the line
Select any point on the line, e.g. the $y$ -axis intercept (0|-2). Go from there 1 to the right and according to the slope $m = \frac{3}{4}$ upwards (alternatively, also the 4-fold length to avoid fractions: 4 to the right and 3 upwards). Connect the two points to get a straight line.
$G_{f}$ has a slope of 0 and intersects the $y$ -axis at 3.

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

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