[tex]y=-\frac{1}{2}x[/tex]
Explanation
a line that passes throught the origin (0,0) is a line in the form
[tex]y=kx[/tex]
where k is the constant , rate of change or slope
so
Step 1
find the constant of the line:
to do that, check any coordiante and replace
a) pick up a coordinate from the line
Let
P(4,2)
so
[tex]\begin{gathered} (4,-2) \\ x\rightarrow4 \\ y=-2 \end{gathered}[/tex]
replace
[tex]\begin{gathered} y=kx \\ -2=4k \\ \text{divide both sides by 4} \\ \frac{-2}{4}=\frac{4k}{4} \\ -\frac{1}{2}=k \end{gathered}[/tex]
therefore, rewriting the function would be
[tex]\begin{gathered} y=kx \\ y=-\frac{1}{2}x \end{gathered}[/tex]
I hope this helps you
