Question

Select the two equations that represent lines perpendicular to the line graphed below:

A) y = -2x + 1
B) y = 1/2x + 4
C) y = 2x - 3
D) y = -4x + 2

Answer 1

None of the equations A, B, C, or D represent lines that are perpendicular to a line with a slope of 3 because their slopes are not the negative reciprocal of 3.

Step-by-step explanation:

To find equations that represent lines perpendicular to a given line, we must identify lines with slopes that are the negative reciprocal of the given line's slope. Suppose the given line has a slope of 3, based on the information provided in the examples. Therefore, we look for lines with a slope of -1/3, which is the negative reciprocal of 3. Looking at the equations provided:

• Equation A: y = -2x + 1, has a slope of -2. This is not the negative reciprocal of 3.

• Equation B: y = 1/2x + 4, has a slope of 1/2. This is also not the negative reciprocal of 3.

• Equation C: y = 2x - 3, has a slope of 2. Again, this is not the negative reciprocal of 3.

• Equation D: y = -4x + 2, has a slope of -4. This slope is a negative reciprocal of the slope 1/4, not 3.

Therefore, none of the options provided represent lines perpendicular to a line with a slope of 3. If the line in the original question had a different slope, we would need that specific information to determine the correct perpendicular lines.