Which graph represents the equation x - 2y = 4?

Rationale

M-58A.png represents the equation x - 2y = 4.

This equation can be rearranged into slope-intercept form (y = mx + b) to identify its graphical representation. By isolating y, we find y = (1/2)x - 2, indicating a slope of 1/2 and a y-intercept of -2, which corresponds to the graph shown in choice A.

A (M-58A.png) CORRECT

This graph correctly depicts the line represented by the equation x - 2y = 4. With a slope of 1/2 and a y-intercept at -2, the line rises gently and crosses the y-axis at the correct point, aligning perfectly with the rearranged equation.

B (M-58B.png) YOUR ANSWER

This graph does not represent the equation correctly, as it shows a steeper slope than 1/2. The line appears to have a slope of approximately 2, which is inconsistent with the given equation. Therefore, this choice is not a correct representation of x - 2y = 4.

C (M-58C.png) YOUR ANSWER

This graph also fails to represent the equation, displaying a horizontal line which suggests a slope of 0. The equation x - 2y = 4 has a positive slope, and thus cannot be represented by a horizontal line.

D (M-58D.png) YOUR ANSWER

This graph depicts a vertical line, indicating an undefined slope. Since the equation x - 2y = 4 is linear with a defined slope of 1/2, a vertical line cannot represent this equation. Therefore, this choice is incorrect.

Conclusion

The graph that accurately represents the equation x - 2y = 4 is M-58A.png, as it correctly illustrates the slope and y-intercept derived from the equation. The other choices misrepresent the equation due to slopes that are either too steep, horizontal, or vertical, further emphasizing the importance of understanding linear equations in graphing.

Which graph represents the equation x - 2y = 4?

M-58A.png represents the equation x - 2y = 4.

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