Question

solve the proportion for y. plug in and write the equivalent proportion of numbers as fractions.
\frac{1}{2} = \frac{y - 6}{y - 16}

Explanation:

Step1: Cross - multiply the proportion

Given the proportion \(\frac{1}{2}=\frac{y - 6}{y-16}\), cross - multiplying (which is based on the property of proportions: if \(\frac{a}{b}=\frac{c}{d}\), then \(a\times d=b\times c\)) gives us \(1\times(y - 16)=2\times(y - 6)\).

Step2: Expand both sides

Expanding the left - hand side and the right - hand side:
Left - hand side: \(y-16\)
Right - hand side: \(2y-12\)
So the equation becomes \(y - 16=2y-12\).

Step3: Solve for y

Subtract \(y\) from both sides of the equation:
\(y - 16-y=2y-12 - y\)
Simplifying, we get \(- 16=y - 12\).
Then add 12 to both sides:
\(-16 + 12=y-12 + 12\)
\(-4=y\)

Answer:

\(y=-4\)