Answer :

To determine the value of [tex]\( y_2 \)[/tex] when given [tex]\( x_1 = 440 \)[/tex], [tex]\( y_1 = 220 \)[/tex], and [tex]\( x_2 = 360 \)[/tex], we can use the property of proportionality. This means that the ratio between [tex]\( x_1 \)[/tex] and [tex]\( y_1 \)[/tex] should be the same as the ratio between [tex]\( x_2 \)[/tex] and [tex]\( y_2 \)[/tex].

First, let's write down the proportional relationship:
[tex]\[ \frac{x_1}{y_1} = \frac{x_2}{y_2} \][/tex]

Substitute [tex]\( x_1 \)[/tex], [tex]\( y_1 \)[/tex], and [tex]\( x_2 \)[/tex] into the equation:
[tex]\[ \frac{440}{220} = \frac{360}{y_2} \][/tex]

Next, simplify the left side of the equation:
[tex]\[ \frac{440}{220} = 2 \][/tex]

Now our equation looks like this:
[tex]\[ 2 = \frac{360}{y_2} \][/tex]

To solve for [tex]\( y_2 \)[/tex], we can multiply both sides of the equation by [tex]\( y_2 \)[/tex]:
[tex]\[ 2y_2 = 360 \][/tex]

Then, isolate [tex]\( y_2 \)[/tex] by dividing both sides by 2:
[tex]\[ y_2 = \frac{360}{2} \][/tex]

This gives:
[tex]\[ y_2 = 180.0 \][/tex]

Therefore, the value of [tex]\( y_2 \)[/tex] is [tex]\( 180.0 \)[/tex].