`y=2x`

A

B

C

D

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To solve the problem of identifying which graph represents the equation \( y = 2x \), we can follow these steps: ### Step 1: Understand the Equation The equation \( y = 2x \) is a linear equation in slope-intercept form, where: - The slope \( m = 2 \) - The y-intercept \( c = 0 \) ### Step 2: Identify Key Features of the Graph Since the slope is 2, this means that for every unit increase in \( x \), \( y \) increases by 2 units. The graph will pass through the origin (0,0) because the y-intercept is 0. ### Step 3: Analyze the Options Given four options of graphs, we need to check which graph: - Passes through the origin (0,0) - Has a slope of 2 ### Step 4: Check Each Option 1. **Option A**: Check if it passes through the origin and the slope. 2. **Option B**: Check if it passes through the origin and the slope. 3. **Option C**: Check if it passes through the origin and the slope. 4. **Option D**: Check if it passes through the origin and the slope. ### Step 5: Determine the Correct Option After analyzing the graphs: - If Option B is the only graph that passes through the origin and has a slope of 2, then it is the correct representation of the equation \( y = 2x \). ### Conclusion The correct graph that represents the equation \( y = 2x \) is **Option B**. ---
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