which best describes the function represented by the table?\n| x | y |\n| ---- | ---- |\n| -2 | -5 |\n| 2 |…

which best describes the function represented by the table?\n| x | y |\n| ---- | ---- |\n| -2 | -5 |\n| 2 | 5 |\n| 4 | 10 |\n| 6 | 15 |\n○ direct variation; $k = \\frac{2}{5}$\n○ direct variation; $k = \\frac{5}{2}$\n○ inverse variation; $k = 10$\n○ direct variation; $k = \\frac{1}{10}$

which best describes the function represented by the table?\n| x | y |\n| ---- | ---- |\n| -2 | -5 |\n| 2 | 5 |\n| 4 | 10 |\n| 6 | 15 |\n○ direct variation; $k = \\frac{2}{5}$\n○ direct variation; $k = \\frac{5}{2}$\n○ inverse variation; $k = 10$\n○ direct variation; $k = \\frac{1}{10}$

Answer

Explanation:

Step1: Check direct variation condition

A direct variation follows $y = kx$, so $k = \frac{y}{x}$.

Step2: Calculate k for each pair

For $x=-2, y=-5$: $\frac{-5}{-2} = \frac{5}{2}$ For $x=2, y=5$: $\frac{5}{2} = \frac{5}{2}$ For $x=4, y=10$: $\frac{10}{4} = \frac{5}{2}$ For $x=6, y=15$: $\frac{15}{6} = \frac{5}{2}$

Step3: Verify inverse variation (eliminate)

Inverse variation follows $xy=k$. For $x=2,y=5$: $25=10$; for $x=4,y=10$: $410=40≠10$, so no inverse variation.

Answer:

direct variation; $k = \frac{5}{2}$