Answer
See explanation
Work Step by Step
The instructions in the question state that the equation of a line passing through the point $(a,0)$ and making an angle $\theta$ with the x-axis is $y=(\tan\theta)(x−a)$.
A line bisecting the first and third quadrants of the graph would have an equation $y=-x$, as seen in the diagram below.
This line passes through the point $(0,0)$ and makes an angle of $135^{\circ}$ with the x-axis.
(This is because as the line bisects the quadrants, it splits the quadrant in half, so each half would have an angle = $\frac{90}{2}$ or $45^{\circ}$, so we can add 45 and 90 together to get the angle the line makes with the x-axis)
So, $a=0$ and $\theta=135^{\circ}$.
Substitute these values into the equation:
$y=(\tan\theta)(x−a)$
$y=(\tan135)(x-0)$
$y=(-1)x$
This equation is the same as the equation mentioned previously, so it does satisfy the equation given in the instructions.
