ANSWER
[tex]\Rightarrow y=\frac{1}{2}|x|[/tex]EXPLANATION
We want to find the absolute value function for the line in blue.
The general form of an absolute value function is:
[tex]y=a|x-h|+k[/tex]where (h, k) = vertex
From the line, the vertex of the graph in blue is:
[tex](0,0)[/tex]To find a, we have to pick a point (x, y) on the line and input it into the general function.
Let us pick (2, 1).
Therefore, we have:
[tex]\begin{gathered} 1=a|2-0|+0 \\ 1=a|2|=2a \\ \Rightarrow a=\frac{1}{2} \end{gathered}[/tex]Therefore, the absolute value function is:
[tex]\begin{gathered} y=\frac{1}{2}|x-0|+0 \\ \Rightarrow y=\frac{1}{2}|x| \end{gathered}[/tex]