Seting up the function term

$m=\frac{3}{4};t=-2m=\backslash frac34;\backslash ;t=-2$

Insert $mm$ and $tt$ into the general line equation $y=mx+ty=mx+t$.

$\Rightarrow y=\frac{3}{4}x-2\backslash Rightarrow\; y=\backslash frac34x-2$

Draw the line

Select any point on the line, e.g. the $yy$-axis intercept (0|-2). Go from there 1 to the right and according to the slope $m=\frac{3}{4}m=\backslash frac34$ 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.

Seting up the function term

$m=0;t=3m=0;\backslash ;t=3$

Insert $mm$ and $tt$ into the general line equation $y=mx+ty=mx+t$.

$\Rightarrow y=3\backslash Rightarrow\; y=3$

Draw the line

The line runs through the $yy$-axis intercept (0|3) parallel to the $xx$-axis because the straight line has a slope of 0.

Seting up the function term

Since the straight line is parallel to the $xx$-axis, its slope is 0 $\Rightarrow m=0\backslash Rightarrow\; m=0$.

The line passes through the point $(-3\mathrm{\mid }-2)(-3\backslash vert-2)$. Since the slope is 0, the line has the $yy$-value -2 at $x=0x=0$.

Its $yy$-axis intercept is therefore at $-2\text{}\Rightarrow t=-2-2\; \backslash Rightarrow\; t=-2$.

$m=0;t=-2m=0;\backslash ;t=-2$

Insert $mm$ and $tt$ into the general line equation $y=mx+ty=mx+t$.

$y=-2y=-2$

Draw the line

The line runs through the $yy$-intercept $(0\mathrm{\mid }-2)(0|-2)$ parallel to the $xx$-axis because the straight line has a slope of 0.

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 $(-4\mathrm{\mid }2)(-4\backslash vert2)$ parallel to the $yy$-axis.