What is the slope of a line that is perpendicular to the line y = -9x + 7?

Rationale

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

The slope of the given line is -9, and the slope of a line perpendicular to another is the negative reciprocal of the original line's slope. Thus, the negative reciprocal of -9 is 1/9, and the corresponding slope of a line perpendicular to it is 19.

A (19) CORRECT

This is the correct answer because the negative reciprocal of -9 (the slope of the given line) is indeed 1/9, which is equivalent to 19 when simplified in terms of slope.

B (-0.111111111) YOUR ANSWER

This choice represents a decimal approximation of the slope -1/9, which is not the negative reciprocal of -9. Hence, this value does not indicate a slope perpendicular to the original line.

C (9) YOUR ANSWER

This option is simply the same value as the negative slope of the original line, which does not correspond to a perpendicular slope. Therefore, it does not satisfy the conditions set by the question.

D (-9) YOUR ANSWER

This choice is the slope of the original line itself. A perpendicular slope must be the negative reciprocal, which -9 is not; hence, this option is incorrect.

Conclusion

In summary, the slope of a line that is perpendicular to another can be found by taking the negative reciprocal of the original slope. In this case, the slope of the original line is -9, so its perpendicular slope is 19. The other options fail to represent a valid perpendicular relationship, confirming that 19 is the accurate answer.

What is the slope of a line that is perpendicular to the line y = -9x + 7?

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

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