which equation represents an inverse variation function that passes through the points (4, 5) and (10…

which equation represents an inverse variation function that passes through the points (4, 5) and (10, 2)?\n$y = \\frac{5}{4}x$\n$y = \\frac{5}{4x}$\n$y = 20x$\n$y = \\frac{20}{x}$

which equation represents an inverse variation function that passes through the points (4, 5) and (10, 2)?\n$y = \\frac{5}{4}x$\n$y = \\frac{5}{4x}$\n$y = 20x$\n$y = \\frac{20}{x}$

Answer

Explanation:

Step1: Recall inverse variation form

The general form of an inverse variation function is $y = \frac{k}{x}$, where $k$ is the constant of variation.

Step2: Solve for $k$ using $(4,5)$

Substitute $x=4$, $y=5$ into $y = \frac{k}{x}$: $5 = \frac{k}{4}$ Multiply both sides by 4: $k = 5 \times 4 = 20$

Step3: Verify with $(10,2)$

Substitute $x=10$, $k=20$ into $y = \frac{k}{x}$: $y = \frac{20}{10} = 2$, which matches the point.

Step4: Match to the option

The function is $y = \frac{20}{x}$.

Answer:

$y = \frac{20}{x}$