A line of two points (4, 2) and (-1, k) is perpendicular to the line y=2x+1, then k = 9/2.
Given a line with equation y = mx + c, the slope is denoted by m.
Given 2 points with slopes m₁ and m₂, those two lines are perpendicular if:
m₁ x m₂ = -1
The given line equation is: y = 2x+1
Hence,
m₁ = 2
Compute the slope from 2 points: (4, 2) and (-1, k)
m₂ = (k - 2) / (-1 - 4)
m₂ = (-1/5) (k - 2)
Use the condition for perpendicular lines:
m₁ x m₂ = -1
2 x (-1/5) (k - 2) = -1
2k - 4 = 5
2k = 9
k = 9/2
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