When X and Y are directly proportional, if X2+6, Y1=4 and Y2=8, what is the value of X1?

To determine the value of (X_1) when (X) and (Y) are directly proportional, it's essential to understand the concept of direct proportionality. This means that the ratio of (X) to (Y) remains constant. Thus, we can express this relationship mathematically as (Y = kX), where (k) is a constant.

Given that (Y_1 = 4) and (Y_2 = 8), we can express their corresponding (X) values using the proportionality constant (k). For the first set, we have the equation:

[

Y_1 = kX_1 \implies 4 = kX_1

]

For the second set, we know:

[

Y_2 = kX_2 \implies 8 = kX_2

]

To find the value of (X_2), we can use the relationship established by direct proportionality:

[

\frac{Y_1}{Y_2} = \frac{X_1}{X_2}

]

Substituting the known (Y) values into this equation gives us:

\