Which of the following is an equation of the line graphed above?

Rationale

y=31x−1 represents the equation of the line graphed above.

The equation indicates a positive slope of 31 and a y-intercept of -1, consistent with the characteristics of the line shown in the graph.

A (y=−31x+1) YOUR ANSWER

This equation suggests a negative slope of -31, which would indicate a steep descent from left to right. However, the graph shows an upward trend, meaning the slope must be positive, disqualifying this option.

B (y=31x−1) CORRECT

This equation correctly describes the line's upward slope of 31 and a y-intercept of -1. It aligns perfectly with the graph's characteristics, confirming that this is the correct representation of the line.

C (y=3x-1) YOUR ANSWER

While this equation has the same y-intercept of -1, it features a much gentler slope of 3. The graph depicts a much steeper incline, indicating this option does not accurately represent the line's steepness.

D (y=-3x-9) YOUR ANSWER

This equation indicates a negative slope of -3 and a y-intercept of -9, suggesting the line would descend sharply from left to right and start much lower on the y-axis. This contradicts the graph's upward trajectory and its position on the coordinate plane.

Conclusion

The equation of the line graphed above must possess a steep positive slope and a specific y-intercept, which is best encapsulated by y=31x−1. Other options either feature incorrect slopes or y-intercepts that misrepresent the line’s behavior as depicted in the graph. Understanding these attributes is essential for accurately interpreting linear equations in the context of graphical representations.

Which of the following is an equation of the line graphed above?

y=31x−1 represents the equation of the line graphed above.

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