Question

which graph represents a function with direct variation?

Explanation:

Step1: Recall Direct Variation Rule

A direct variation function has the form \( y = kx \), where \( k \) is a constant. Its graph is a straight line passing through the origin \((0,0)\).

Step2: Analyze Each Graph

• First graph: Does not pass through \((0,0)\) (y-intercept non - zero).
• Second graph: Passes through the origin \((0,0)\) and is a straight line, so it could be \( y = kx \).
• Third graph: Does not pass through \((0,0)\) (y - intercept non - zero).
• Fourth graph: Passes through \((0,0)\) and is a straight line. Wait, but let's check the slope. Wait, the second graph: Let's confirm. The equation of direct variation is \( y=kx \), so when \( x = 0 \), \( y=0 \). The second graph (middle top) passes through \((0,0)\), and is a straight line. The fourth graph (bottom right) also passes through \((0,0)\). Wait, maybe I mis - saw. Wait, the second graph (the middle one in the top row) has a line passing through the origin. Let's re - check. The first graph: y - intercept is 1 (since it crosses y - axis at (0,1)), so not direct variation. The second graph: crosses at (0,0), so \( y=kx \) form. The third graph: y - intercept is - 2, so not. The fourth graph: Let's see, when \( x = 0 \), \( y = 1 \)? Wait no, the fourth graph (bottom right) seems to cross y - axis at (0,1)? Wait no, maybe the second graph (middle top) is the one. Wait, the direct variation graph must pass through the origin. So the second graph (the middle one in the top row, with the circle below it) passes through (0,0), so it's a direct variation graph.

Answer:

The Middle Graph (the second graph in the top row, with the circle below it)