What is the slope of a line perpendicular to the line given by the equation 5x - 2y = -10?
To find the slope of a line perpendicular to the given line, we first determine the slope of the original line, which is 0.4, making the slope of the perpendicular line -2.5.
To find the slope of a line from its equation, we need to rearrange it into slope-intercept form (y = mx + b). For the equation 5x - 2y = -10, the slope is m = 0.4. The slope of a line perpendicular to this will be the negative reciprocal, which is -2.5.
This choice represents the same slope as the original line, not the perpendicular slope. The slope of the original line (0.4) and its negative reciprocal (-2.5) are distinct, thus -0.4 cannot be the slope of a line perpendicular to the line given by the equation.
This slope does not represent a negative reciprocal of 0.4. The correct slope of the perpendicular line is -2.5, which is obtained by taking the negative reciprocal of the original slope. A slope of 25 would indicate a steep upward incline, which is not relevant in this context.
Similar to choice B, a slope of 52 does not correspond to the negative reciprocal of 0.4. The perpendicular slope must be -2.5, which means this option is also irrelevant as it does not satisfy the perpendicularity condition.
This is the correct choice as it is the negative reciprocal of the original slope of 0.4. The negative reciprocal is calculated as -1/(0.4), leading us to -2.5, which indicates the slope of the line that is perpendicular to the given line.
To summarize, the slope of a line perpendicular to one described by the equation 5x - 2y = -10 is -2.5, derived from the negative reciprocal of the original line's slope of 0.4. The other options either represent the same slope, do not meet the negative reciprocal requirement, or are unrelated, confirming that -2.5 is the valid answer.
Related Questions
View allThe manager of a shipping company plans to use a small truck to ship p...
Multiply: (x² - 3)(x^5 + 2x^3)
The manager of a shipping company plans to use a small truck to ship p...
John and Mike are participating in a long-distance bicycling event. Mi...
A manufacturing plant makes dog toys in the shape of a sphere. The dia...
Related Quizzes
View allGED Mathematical Reasoning
Mathematical Reasoning GED
GED Reasoning Through Language Arts
GED Reasoning Through Language Arts Practice Test
GED Science Sample Test
GED Science Test Prep
Sample GED Social Studies Test
Social Studies GED Test
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations