Answer:
[tex]k=-2[/tex]
Step-by-step explanation:
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]
a) For [tex]x=-1[/tex]
[tex]f(x)=2[/tex]
Find the value of k
[tex]f(x)/x=k[/tex] ------> substitute the values
[tex]k=2/-1=-2[/tex]
b) For [tex]x=2[/tex]
[tex]f(x)=-4[/tex]
Find the value of k
[tex]f(x)/x=k[/tex] ------> substitute the values
[tex]k=-4/2=-2[/tex]
c) For [tex]x=5[/tex]
[tex]f(x)=-10[/tex]
Find the value of k
[tex]f(x)/x=k[/tex] ------> substitute the values
[tex]k=-10/5=-2[/tex]
therefore
[tex]k=-2[/tex]
