Parallel to the $x$-axis, means that the slope is $m=0$.

Plug $m$ and $P$ 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 $m$ into the straight line equation in order to calculate $t$.

Plug $m$ and $t$ into the general equation of a straight line.

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

The straight line can therefore only be described as the $x$-value of $R$.

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 $1$.

Substitute $m$ and $S$ into the general line equation and solve for $t$.

Substitute $m$ and $t$ into the general line equation.

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

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

Calculate the slope $m$ using the difference quotient .

Substitute $m$ and $t$ into the general line equation.