Question 12

The slope of the line represented by the table is -2.

The slope of the line is calculated based on the change in the y-values divided by the change in the x-values between two points. In this case, the slope is determined to be -2 based on the data provided in the table.

A) -4

This option is incorrect as it suggests a steeper negative slope than what is represented in the table. The calculations do not support a change in y-values that would yield a slope of -4, indicating a misinterpretation of the data.

B) -2.5

Option B is also incorrect. A slope of -2.5 implies a different rate of change that does not align with the values from the table. The ratio of the changes in y and x does not reflect this value.

C) -2

This is the correct answer. The slope of -2 indicates that for every unit increase in x, the y-value decreases by 2 units, which accurately reflects the relationship shown in the table data.

D) -0.5

Option D is incorrect as it proposes a much shallower slope than what the table indicates. A slope of -0.5 would suggest that the line rises more than it falls, which contradicts the negative trend revealed in the table.

Conclusion

The correct option, -2, effectively represents the consistent rate of change between the x and y values in the table. Other options fail to accurately depict the relationship, either suggesting too steep or too shallow a slope, thereby misrepresenting the data's intended slope.