Question:medium

In a population, the frequency of an allele changes with time as shown in the table below.
Year (x)010203040
Allele frequency (y)0.10.20.30.40.5
Which one of the following describes how allele frequency changes with year?

Show Hint

Find the slope from any two points in the table, then check which equation matches both the slope and the intercept.
Updated On: Jul 20, 2026
  • \(y = 0.01x + 0.1\)
  • \(x = y + 0.1\)
  • \(x = 0.1 + 0.01y\)
  • \(y = x + 0.1\)
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Set up the general line.
A straight line through the data can be written as $y = mx + c$, where $m$ is the slope and $c$ is the value of $y$ when $x=0$.

Step 2: Read $c$ straight off the table.
When the year $x=0$, the table already gives $y=0.1$. So $c=0.1$ without any extra work.

Step 3: Get $m$ from the two ends of the table.
Using the first point $(0, 0.1)$ and the last point $(40, 0.5)$,
\[ m=\frac{0.5-0.1}{40-0}=\frac{0.4}{40}=0.01 \]

Step 4: Write the fitted line.
\[ y=0.01x+0.1 \]

Step 5: Confirm with a middle row, not just the ends.
At $x=20$, the formula gives $y=0.01(20)+0.1=0.3$, exactly the value the table shows. This confirms the fit is not a coincidence of the endpoints.

Step 6: Reject the flipped options.
Options that write $x$ in terms of $y$, like $x=y+0.1$ or $x=0.1+0.01y$, mix up which variable is doing the changing. Since year is the input and allele frequency is the output here, $y$ should be written in terms of $x$, not the other way round, and neither flipped option even satisfies the table's numbers when tested directly.

Step 7: Conclude.
\[ \boxed{y=0.01x+0.1} \]
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