Answer:
Given points: (1,4) and (2,8)
Direct Variation:
The statement y varies directly as x, which means that when x increases, y increases by the same factor.
In other words we can say that, y and x always have the same ratio;
i.e, [tex]\frac{y}{x} = k[/tex] ; where k is the constant of variation.
or we can write this as : [tex]y=kx[/tex] ......[1]
Substitute the value of given points in [1];
For (1,4)
put x =1 and y = 4 we get;
[tex]4= k(1)[/tex]
or
k =4
For(2,8)
put x = 2 and y= 8 in [1];
[tex]8=k(2)[/tex]
Divide both sides by 2;
4 = k or k =4
As you can see that a direct variation goes through the points (1,4) and (2,8) , the constant variation in both cases is, k =4.
