which best describes the function on the graph?○ direct variation; $k = 3$○ direct variation; $k =…

which best describes the function on the graph?○ direct variation; $k = 3$○ direct variation; $k = \\frac{1}{3}$○ inverse variation; $k = 3$○ inverse variation; $k = \\frac{1}{3}$

which best describes the function on the graph?○ direct variation; $k = 3$○ direct variation; $k = \\frac{1}{3}$○ inverse variation; $k = 3$○ inverse variation; $k = \\frac{1}{3}$

Answer

Explanation:

Step1: Identify variation type

Direct variation graphs are straight lines passing through the origin $(0,0)$, which matches the given graph. Inverse variation graphs are hyperbolas, so we eliminate inverse variation options.

Step2: Find direct variation constant

Direct variation follows $y = kx$. Pick a point on the line, e.g., $(3,1)$. Substitute into the formula: $1 = k \times 3$ Solve for $k$: $k = \frac{1}{3}$

Answer:

direct variation; $k = \frac{1}{3}$