Question

A biologist recorded $11$ snakes on $24$ acres in one area and $13$ snakes on $49$ acres in another area. Find a linear equation that models the number of snakes in $x$ acres.

• A. $y=x+13$
• B. $y=\frac{2}{25}x-\frac{227}{25}$
• C. $y=\frac{25}{2}x+\frac{25}{227}$
• D. $y=\frac{2}{25}x+\frac{227}{25}$

Answer 1

Answer: (D)

$y=\frac{2}{25}x+\frac{227}{25}$

Let us consider that the number of snakes vary linearly with the acres of land.
Let the acres of land be denoted by x and the number of snakes be denoted by y; then it passes through $(24,11)$ and $(49,13)$.
Therefore the equation of the model line is
$\frac{y-13}{x-49}=\frac{y-11}{x-24}$
Or
$-24y-13x+312=-11x-49y+539$
$25y=2x+227$
Or
$y=\frac{2x}{25}+\frac{227}{25}$