To determine the value of [tex]\( y_2 \)[/tex] given the values [tex]\( x_1 = 440 \)[/tex], [tex]\( y_1 = 220 \)[/tex], and [tex]\( x_2 = 316 \)[/tex], we can assume a linear relationship between the given pairs of values.
The values [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are directly proportional, meaning the ratio between the pairs should remain constant. Hence, we set up a proportion between the given pairs of values:
[tex]\[
\frac{y_1}{x_1} = \frac{y_2}{x_2}
\][/tex]
Given:
[tex]\[
x_1 = 440, \quad y_1 = 220, \quad x_2 = 316
\][/tex]
We substitute the given values into the proportion:
[tex]\[
\frac{220}{440} = \frac{y_2}{316}
\][/tex]
To solve for [tex]\( y_2 \)[/tex], we first simplify the fraction on the left side of the equation:
[tex]\[
\frac{220}{440} = \frac{1}{2}
\][/tex]
Now, the equation becomes:
[tex]\[
\frac{1}{2} = \frac{y_2}{316}
\][/tex]
Next, we solve for [tex]\( y_2 \)[/tex] by multiplying both sides of the equation by 316:
[tex]\[
y_2 = \frac{1}{2} \times 316 = 158
\][/tex]
Therefore, the value of [tex]\( y_2 \)[/tex] is:
[tex]\[
y_2 = 158.0
\][/tex]
