1. The problem is to match the equation $y=2^x$ with its correct graph. 2. The equation $y=2^x$ represents an exponential function with base 2. 3. Exponential functions of the form $y=a^x$ where $a>1$ have these properties: - The graph passes through the point $(0,1)$ because $2^0=1$. - The function is always positive, so the graph lies above the $x$-axis. - The graph is increasing, rising steeply to the right and approaching the $x$-axis as $x$ goes to negative infinity. 4. The description of the graph: an increasing line passing through the origin heading upward from left to right. 5. The graph of $y=2^x$ does not pass through the origin $(0,0)$, it passes through $(0,1)$. 6. Therefore, the graph described does NOT match $y=2^x$. The correct graph of $y=2^x$ should pass through $(0,1)$ and be an increasing curve, not a line through the origin. Final conclusion: The graph described as passing through the origin is not the correct graph for $y=2^x$.