Question

Determine which of these three lines are parallel, perpendicular, or neither. Make sure you show your work and explain your answer. y=-2x+1 4x-2y=10 4x+2y=10.

a. Lines 1 and 3 are parallel.
b. Lines 1 and 2 are neither parallel nor perpendicular.
c. Lines 2 and 3 are neither parallel nor perpendicular.
d. All

Answer 1

Lines 1 and 3 are parallel since they both have a slope of -2. Lines 1 and 2 are perpendicular as their slopes are negative reciprocals of each other. Lines 2 and 3 are neither parallel nor perpendicular as their slopes are different and not negative reciprocals.

Step-by-step explanation:

To determine which lines are parallel, perpendicular, or neither, we must find the slope of each line:

• The slope of the first line, y = -2x + 1, is -2.
• For the second line, 4x - 2y = 10, we rearrange to the slope-intercept form (y = mx + b) to find the slope: y = 2x - 5, so the slope is 2.
• The third line, 4x + 2y = 10, can also be rearranged to y = -2x + 5, giving us a slope of -2.

Comparing these slopes, we see the following:

• Lines 1 and 3 have the same slope (-2), therefore they are parallel.
• Lines 1 and 2 have slopes that are negative reciprocals of each other (-2 and 2), therefore they are perpendicular.
• Lines 2 and 3 have different slopes (2 and -2) and are not negative reciprocals, so they are neither parallel nor perpendicular.