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].
