Exercises: Drawing graphs of linear functions

Draw the graph of the linear functions in a coordinate system!

$f (x) = - 2 x + 4$

For this task you need the following basic knowledge: Slope/Gradient of a line
Drawing the linear function
First read off the $y$ -intercept and the slope from the function term of the linear function.
In this case:
$f (x) = - 2 x + 4$
You obtain a $y$ -intercept of $t = 4$ and a slope of $m = - 2$ .
First draw the intersection with the $y$ -axis that results from the $y$ -axis intercept. This is at $A (0 / 4)$ .
Then draw a gradient triangle using the gradient. To do this, go one length unit to the right and two length units down. This gives you the point $B = (1 / 2)$ . Now draw the straight line through points $A$ and $B$ .
You obtain the graph $G_{f}$ of $f (x)$ .
$g (x) = \frac{1}{2} x - 2$

For this task you need the following basic knowledge: Slope/Gradient of a line
Drawing the linear function
First read off the $y$ -intercept and the slope from the function term of the linear function.
In this case:
$f (x) = \frac{1}{2} x - 2$
You obtain a $y$ -intercept of $t = - 2$ and a slope of $m = \frac{1}{2}$ .
First draw the intersection with the $y$ -axis that results from the $y$ -axis intercept. This is at $C (0 / - 2)$ .
Then draw a gradient triangle using the gradient. To do this, go one length unit to the right and two length units down. This gives you the point $D = (2 / - 1)$ . Now draw the straight line through points $C$ and $D$ .
You obtain the graph $G_{g}$ of $g (x)$ .
$h (x) = 5$

For this task you need the following basic knowledge: Slope/Gradient of a line
Drawing the linear function
The function $h (x) = 5$ represents a special case of a linear function. The slope of $h (x)$ is $0$ .
This means that the function value does not change regardless of the variable $x$ .
So if you draw the function value $h (x) = 5$ for each $x$ in a coordinate system, you get a straight line that runs parallel to the $x$ axis at the height $y = 5$ .

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Exercises: Drawing graphs of linear functions

Drawing the linear function

Drawing the linear function

Drawing the linear function