Question

One plane flies across the country with a path modeled on a map by the equation 2x−7y=−25. Select all the equations for lines that could represent perpendicular flight paths.

Option 1: y=27x−6
Option 2: 7x+2y=−10
Option 3: y−13=72(x+8)
Option 4: 14x+4y=41
Option 5: 7y=2x+5

Answer 1

To determine if two lines are perpendicular, we check if their slopes are negative reciprocals. The given line has a slope of 2/7. Option 2 (7x + 2y = -10) and option 4 (14x + 4y = 41) have slopes that are negative reciprocals of the given line's slope, making them perpendicular flight paths.

Step-by-step explanation:

We can determine if two lines are perpendicular by checking if their slopes are negative reciprocals of each other. The equation of the given line is 2x - 7y = -25. To find the slope of this line, we rearrange the equation to solve for y and write it in slope-intercept form (y = mx + b), where m is the slope. Rearranging the equation, we get:

2x - 7y = -25

-7y = -2x - 25

y = (2/7)x + 25/7

Therefore, the slope of the given line is 2/7.

Now, let's check the slopes of the options given:

1. y = 27x - 6, slope = 27
2. 7x + 2y = -10, slope = -7/2
3. y - 13 = 72(x + 8), slope = 72
4. 14x + 4y = 41, slope = -14/4 = -7/2
5. 7y = 2x + 5, slope = 2/7

Based on the slopes, the equations that could represent perpendicular flight paths to the given line with equation 2x - 7y = -25 are option 2: 7x + 2y = -10 and option 4: 14x + 4y = 41.