y=x
Explanation
f(x)=?
Step 1
the angle bisector is the line or line segment that divides the angle into two equal parts, then we have half of 90 degrees
if you know the angle formed by a line with x-axis you can find the slope using:
[tex]\begin{gathered} \text{slope}=\tan \alpha\text{ }\cdot \\ \end{gathered}[/tex]replace
[tex]\begin{gathered} \alpha=45\~ \\ \text{slope}=\tan \text{ 45=1} \\ \text{slope =1} \end{gathered}[/tex]now, we have the slope of the line
Step 2
Also, the line crosses the origin(0,0), then, we have a point of the line
Step 3
fin the equation using
slope=1
point of the line (0,0)
[tex]\begin{gathered} y-y_0=m(x-x_0) \\ \text{where} \\ m\text{ is the slope } \\ (x_1,y_1)\text{ are the coordinates of the known point} \end{gathered}[/tex]replace
[tex]\begin{gathered} y-0=1(x-0) \\ y-0=1x-1\cdot0 \\ y=1x \\ y=x \end{gathered}[/tex]so, the equation is y=x
