Final answer:
The equations that represent lines perpendicular to y = -(4/5)x + 2 are the ones with slopes that are the negative reciprocals of the original slope. The equations 5x + 4y = 28 and 4y - 5x = -12 have the slope of 5/4, which is the negative reciprocal of -4/5, making them perpendicular to the given line.
Step-by-step explanation:
The question asks which equation represents a line that is perpendicular to the line y = -(4/5)x + 2. To find a line that is perpendicular, we look for a line with a slope that is the negative reciprocal of the original line's slope. Since the slope of the given line is -4/5, the slope of the perpendicular line must be 5/4.
Now, let's analyze the given choices:
- 5x + 4y = 28: To find the slope, we rearrange to y = -5/4x + 7, which has the correct slope of 5/4.
- 4x - 5y = -25: Rearranging to y = 4/5x + 5, which has a slope of 4/5, not perpendicular to the original line.
- 4y - 5x = -12: Rearranging to y = 5/4x - 3, which has the correct slope of 5/4.
- 4x + 5y = -30: Rearranging to y = -4/5x - 6, which has a slope of -4/5, not perpendicular to the original line.
Therefore, the equations 5x + 4y = 28 and 4y - 5x = -12 both represent lines that are perpendicular to y = -(4/5)x + 2 because they both have a slope of 5/4.