Line k has slope -2 and passes through point (3, -1). Quantity A: The x-intercept of line k, Quantity B: The y-intercept of line k

Rationale

Quantity B is greater.

To find the intercepts of line k with a slope of -2 that passes through the point (3, -1), we can determine that the y-intercept will be greater than the x-intercept. This is because the line's negative slope indicates it will cross the y-axis at a higher value than it does the x-axis.

A (Quantity A is greater.) YOUR ANSWER

The x-intercept can be calculated by setting y to 0 in the line equation \( y = -2x + b \). Substituting the known point (3, -1) allows us to find the y-intercept (b) as 5. Setting y to 0 gives an x-intercept of 2. Since the y-intercept (5) is greater than the x-intercept (2), this option is incorrect.

B (Quantity B is greater.) CORRECT

As established, the y-intercept is determined to be 5, while the x-intercept is found to be 2. Since 5 is indeed greater than 2, this choice accurately reflects the relationship between the two quantities.

C (The two quantities are equal.) YOUR ANSWER

For the two quantities to be equal, both intercepts would need to have the same value. However, we calculated the y-intercept as 5 and the x-intercept as 2, demonstrating they are not equal. Therefore, this option is incorrect.

D (The relationship cannot be determined from the information given.) YOUR ANSWER

The information provided is sufficient to calculate both intercepts explicitly. We have determined that the y-intercept is 5 and the x-intercept is 2. Thus, this choice is also incorrect, as the relationship can be clearly established.

Conclusion

The calculated intercepts of line k illustrate that the y-intercept (5) is greater than the x-intercept (2). This definitive relationship confirms that Quantity B is greater than Quantity A, demonstrating that the slope and the point through which the line passes provide enough information to determine the intercepts accurately.

Line k has slope -2 and passes through point (3, -1). Quantity A: The x-intercept of line k, Quantity B: The y-intercept of line k

Quantity B is greater.

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