Question

Select the equations that are parallel and perpendicular to y = 2x − 1 and that pass through the point (4, 1).

parallel: y = 2x − 7
perpendicular: y = -1/2x + 3

parallel: y = 2x + 2
perpendicular: y = -1/2x+ 4 1/2

parallel: y = -1/2x − 7
perpendicular: y = 2x + 3

parallel: y = −2x − 7
perpendicular: y = -1/2x − 1

Answer 1

parallel lines have the same slope, so we know the slope will be 2.
y - y1 = m(x - x1)...using slope 2 and points(4,1)
y - 1 = 2(x - 4)
y - 1 = 2x - 8
y = 2x - 8 + 1
y = 2x - 7 <-- this is your parallel line

perpendicular lines have negative reciprocal slopes which means your slope will be -1/2.
y - y1 = m(x - x1)...using slope -1/2 and points (4,1)
y - 1 = -1/2(x - 4)
y - 1 = -1/2x + 2
y = -1/2x + 2 + 1
y = -1/2x + 3 <-- this is your perpendicular line