Question 28

The graph that shows a line described by 4x - 3y = 12 is D.

This equation represents a linear relationship between x and y. The correct graph, D, accurately depicts the line formed by the equation when plotted on a Cartesian coordinate system.

A) M-97A.png

Graph A does not represent the equation 4x - 3y = 12 as it fails to meet the necessary slope and y-intercept derived from rearranging the equation into slope-intercept form. The line depicted in this graph does not intersect the correct points that satisfy the equation.

B) M-97B.png

Graph B also does not correctly illustrate the equation 4x - 3y = 12. It likely has a different slope and intercept, indicating that it does not align with the linear relationship dictated by the equation provided.

C) M-97C.png

Graph C is incorrect as well, as it does not represent the line described by the equation 4x - 3y = 12. The orientation and position of the line in this graph do not correspond to the calculated values derived from the equation.

D) M-97D.png

Graph D accurately represents the line described by the equation 4x - 3y = 12. Upon converting the equation to slope-intercept form (y = (4/3)x - 4), it is evident that this graph correctly depicts the slope and intercept corresponding to the equation.

Conclusion

Graph D is definitively the correct representation of the equation 4x - 3y = 12, as it aligns with the calculated slope and intercept. All other options fail to accurately capture the linear relationship described by the equation, confirming that D is the only viable choice.