Parallel to the $xx$-axis, means that the slope is $m=0m\; =\; 0$.

Plug $mm$ and $PP$ into the general line equation.

Assemble to a line equation.

Parallel to the bisector of the 2nd quadrant means the line has the same slope as the bisector.

The slope of the bisector of the 2nd quadrant is -1

Plug $mm$ into the straight line equation in order to calculate $tt$.

Plug $mm$ and $tt$ into the general equation of a straight line.

Parallel to the $yy$-axis means that there is no function equation, since an $xx$-value is assigned an infinite number of $yy$-values.

The straight line can therefore only be described as the $xx$-value of $RR$.

The line being parallel to the bisector of the 1st quadrant means it has the same slope.

The slope of the bisector of the 1st quadrant is $11$.

Substitute $mm$ and $SS$ into the general line equation and solve for $tt$.

Substitute $mm$ and $tt$ into the general line equation.

Passing through the origin means, the $yy$-axis intercept is $t=0t=0$.

Being parallel to the straight line $\overline{\mathrm{A}\mathrm{B}}\backslash overline\{\backslash mathrm\{AB\}\}$ means that the line has the same slope as $\overline{\mathrm{A}\mathrm{B}}\backslash overline\{\backslash mathrm\{AB\}\}$.

Calculate the slope $mm$ using the difference quotient .

Substitute $mm$ and $tt$ into the general line equation.