Exercises: Drawing graphs of linear functions

Draw the graphs of the functions with the following equation:

$y = 3 x - 2$

For this task you need the following basic knowledge: Linear function
Determine one point
$y = 3 x - 2$
$- 2$ is the $t$ within the general line equation, or in other words, the $y$ -axis intercept.
$\Rightarrow P (0 | - 2)$
Find the slope
Determine the slope $m$ of the function
$y = 3 x - 2$
$3$ is the $m$ within the general line equation, or in other words, the slope.
$m = 3$
Draw the line
Go from the previously determined point one unit to the right and $3$ upwards, since $m$ is equal to $3$ . Here is a second point of the function.
Then connect the two points to form a straight line.
$y = 2 - x$

For this task you need the following basic knowledge: Linear function
Transform the equation
$y = 2 - x$
First, we do a little transformation, such that we get the form of a general line equation.
$y = - x + 2$
Determine one point
$y = - x + 2$
$+ 2$ is the $t$ within the general line equation, or in other words, the $y$ -axis intercept.
$\Rightarrow P (0 | 2)$
Find the slope
Determine the slope $m$ of the function
$y = - x + 2$
$- 1$ is the $m$ within the general line equation, or in other words, the slope.
$m = - 1$
Draw the line
From the previously determined point, go one unit to the right and $1$ downwards, since $m$ is negative. Here is a second point of the function.
Then connect the two points to form a straight line.
$y = - \frac{3}{4} x - 1$

For this task you need the following basic knowledge: Linear function
Determine one point
$y = - \frac{3}{4} x - 1$
$- 1$ is the $t$ within the general line equation, or in other words, the $y$ -axis intercept.
$\Rightarrow P (0 | - 1)$
Find the slope
Determine the slope $m$ of the function
$y = - \frac{3}{4} x - 1$
$- \frac{3}{4}$ is the $m$ within the general line equation, or in other words, the slope.
$m = - \frac{3}{4}$
Draw the line
From the previously determined point, go one unit to the right and $\frac{3}{4}$ downwards, since $m$ is negative. Here is a second point of the function.
Then connect the two points to form a straight line.
$y = - \frac{1}{2} x + 2$

For this task you need the following basic knowledge: Linear function
Determine one point
$y = - \frac{1}{2} x + 2$
$+ 2$ is the $t$ within the general line equation, or in other words, the $y$ -axis intercept.
$\Rightarrow P (0 | 2)$
Find the slope
Determine the slope $m$ of the function
$y = - \frac{1}{2} x + 2$
$- \frac{1}{2}$ is the $m$ within the general line equation, or in other words, the slope.
$m = - \frac{1}{2}$
Draw the line
From the previously determined point, go one unit to the right and $\frac{1}{2}$ downwards, since $m$ is negative. Here is a second point of the function.
Then connect the two points to form a straight line.
$y = \frac{3}{4} x + 1$

For this task you need the following basic knowledge: Linear function
Determine one point
$y = \frac{3}{4} x + 1$
$1$ is the $t$ within the general line equation, or in other words, the $y$ -axis intercept.
$\Rightarrow P (0 | 1)$
Find the slope
Determine the slope $m$ of the function
$y = \frac{3}{4} x + 1$
$\frac{3}{4}$ is the $m$ within the general line equation, or in other words, the slope.
$m = \frac{3}{4}$
Draw the line
From the previously determined point go one unit to the right and $\frac{3}{4}$ upwards, since $m$ is positive. Here is a second point of the function.
Then connect the two points to form a straight line.