The correct answer between all the choices given are the letters B and E. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.
Answer:
B. [tex](3,15)[/tex]
E. [tex](-1,-5)[/tex]
Step-by-step explanation:
we have
[tex]y=5x[/tex] -----> represent a linear direct variation
we know that
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]
In this problem we have
[tex]k=y/x=5[/tex]
Verify each case
Point A [tex](0,1)[/tex]
[tex]k=y/x=1/0[/tex] ----> k is undefined
Point B [tex](3,15)[/tex]
[tex]k=y/x=15/3=5[/tex] -----> the point is on the given line
Point C [tex](4,2)[/tex]
[tex]k=y/x=2/4=0.5[/tex] -----> the point is not on the given line
Point D [tex](3,6)[/tex]
[tex]k=y/x=6/3=2[/tex] -----> the point is not on the given line
Point E [tex](-1,-5)[/tex]
[tex]k=y/x=-5/-1=5[/tex] -----> the point is on the given line
Point F [tex](-1,5)[/tex]
[tex]k=y/x=5/-1=-5[/tex] -----> the point is not on the given line
