Answer: [tex]y=6x[/tex]
Step-by-step explanation:
The equation that shows directly proportional relationship between the two variables x and y is given by :-
[tex]y=kx[/tex] (1)
Using table , first substitute y=24 for x=4
[tex]24=k(4)\\\\\Rightarrow\ k= \dfrac{24}{4}=6\\\\\Rightarrow\ k=6[/tex]
We can check further
For y=7 for x=42
[tex]42=k(7)\\\\\Rightarrow\ k= \dfrac{42}{7}=6\\\\\Rightarrow\ k=6[/tex]
Substitute the value of k in the equation (1) , we get the equation represents the proportional relationship displayed in the table :-
[tex]y=6x[/tex]
Hence, the correct answer is [tex]y=6x[/tex]
