Here, we are required to determine the equation of the line u which is perpendicular to the line t and passes through the point (8,8).
The equation of the line u is;. y = (-x/4) + 10.
First, the product of the slope of 2 perpendicular lines is negative 1 i.e -1.
M1 × M2 = -1
From observation, the slope of line t given by y = 4x - 8 is equal to 4.
- Therefore, since M1 = 4,
- Then, M2 = -1/4
To get the equation of a line,
Slope, M2 = (y - y1)/(x - x1)
where M2 = -1/4 , y1 = 8 and x1 = 8.
Therefore, -1/4 = (y - 8)/(x - 8).
Therefore, -x + 8 = 4y -32
Therefore, 4y = -x + 40.
Ultimately, the equation of the line u is ;
y = (-x/4) + 10.
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