Question 5

The slope of a line perpendicular to the given line is 25.

To find the slope of a line perpendicular to the line represented by the equation 5x - 2y = -10, we first need to determine the slope of the given line, which is 0.04. The slope of a line perpendicular to it is the negative reciprocal, resulting in a slope of 25.

A) -0.4

This option is incorrect because -0.4 does not represent the negative reciprocal of the slope of the original line. The calculated slope of the line from the equation is 0.04, and its negative reciprocal is 25, not -0.4.

B) 25

This option is correct. The slope of the line given by the equation 5x - 2y = -10 is 0.04. The negative reciprocal of 0.04 is indeed 25, making this the slope of the line that is perpendicular to the original line.

C) 52

This option is incorrect as 52 is not the correct negative reciprocal of the slope of the original line. The correct calculation leads to a perpendicular slope of 25, and 52 is significantly larger than this value.

D) -2.5

This option is also incorrect. The negative reciprocal of the slope 0.04 is 25, not -2.5. Therefore, this option does not satisfy the condition of being the slope of the line perpendicular to the given line.

Conclusion

The correct answer is 25, as it accurately represents the negative reciprocal of the slope of the original line. All other options fail to provide the correct perpendicular slope, confirming that only option B aligns with the mathematical principles governing slopes of perpendicular lines.