Answer :
The required equation of the line is y = 4x + 1.
Slope-Intercept form of a line:
The Slope-intercept form of a line is given by
y = mx + c
Where m is the slope of the line and c is the y-intercept
Note:
The product of slopes of perpendicular lines = -1
Here we have
y = -1/4x + 6 Line (1)
Here slope of the line m₁ = -1/4
Let y = m₂x + c Line (2)
Assume that Line (2) is the perpendicular line to Line
As we know The product of slope of two perpendicular lines is -1
=> m₁m₂ = -1 [∵ Line (1) and Line (2) perpendicular lines ]
=> -1/4(m₂) = -1 [ ∵ m₁ = -1/4 ]
=> m₂ = 4
The line (2) => y = 4x + c
Given that the line passes through (2, 9)
=> 9 = 4(2) + c
=> c = 9 - 8
=> c = 1
Therefore,
The required equation of the line is y = 4x + 1
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