Which graph shows a line described by 4x - 3y = 12?

Rationale

Graph D shows a line described by 4x - 3y = 12.

The equation 4x - 3y = 12 can be rearranged into slope-intercept form (y = mx + b) to identify the correct graph. By isolating y, we find that y = (4/3)x - 4, indicating a slope of 4/3 and a y-intercept of -4, which matches the characteristics of graph D.

A (M-97A.png) YOUR ANSWER

This graph does not accurately represent the equation 4x - 3y = 12. The slope and intercept do not match those derived from the equation; specifically, the line appears to have a different slope and crosses the y-axis at a value inconsistent with -4.

B (M-97B.png) YOUR ANSWER

Graph B fails to depict the correct slope and y-intercept. The line in this graph appears to have a negative slope, while the equation has a positive slope of 4/3. Additionally, its y-intercept does not align with the expected value of -4.

C (M-97C.png) YOUR ANSWER

Graph C also does not represent the line described by the equation. While it has a positive slope, it does not correspond to the slope of 4/3, and its y-intercept does not match -4, confirming it is not the correct representation of the given equation.

D (M-97D.png) CORRECT

This graph accurately reflects the line described by 4x - 3y = 12. The slope of 4/3 and the y-intercept of -4 are correctly represented, aligning perfectly with the rearranged form of the equation.

Conclusion

To solve for the correct graph representing the equation 4x - 3y = 12, we analyze the slope and y-intercept derived from the equation. Graph D is the only option that accurately reflects the slope of 4/3 and the y-intercept of -4, confirming it as the proper representation of the line defined by the equation. The other graphs fail to match these critical characteristics.

Which graph shows a line described by 4x - 3y = 12?

Graph D shows a line described by 4x - 3y = 12.

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