Question 9

The slope of a line that is perpendicular to the line y = -9x + 7 is 19.

To find the slope of a line that is perpendicular to another, we must take the negative reciprocal of the original line's slope. The line y = -9x + 7 has a slope of -9, so the negative reciprocal is 19.

A) 19

This option is correct because the negative reciprocal of -9 is indeed 19. Therefore, a line that is perpendicular to the given line will have this slope.

B) -0.111111111

This option is incorrect because -0.111111111 does not reflect the negative reciprocal of -9. The correct negative reciprocal is 19, making this option not applicable.

C) 9

This option is also incorrect because 9 is not the negative reciprocal of -9. Instead, the reciprocal of -9 is -1/9, and its negative reciprocal is 19, which does not match this option.

D) -9

This option is incorrect as well. While -9 is the slope of the original line, it does not represent the slope of a line that is perpendicular to it. The correct perpendicular slope is 19.

Conclusion

The correct answer is 19 because it is the negative reciprocal of the slope of the original line, -9. All other options fail to represent the necessary mathematical relationship required for perpendicular slopes. Therefore, 19 is definitively the only correct answer in this context.