Which equation is the equation of a line that passes through (-6, 4) and is perpendicular to y=6×-2?
A. y = -6× - 32
B. y = -1/6× + 3
C. y = 1/6× + 5
D. y = 6× + 40
The equation of a line that is perpendicular to y=6×-2 will have a slope that is the negative reciprocal of 6, which is -1/6.
Using the point-slope form of a linear equation, the equation can be written as:
y - y1 = m(x - x1)
where (x1, y1) are the coordinates of a point on the line, and m is the slope.
Plugging in the values (-6, 4) and m = -1/6:
y - 4 = -1/6(x - (-6))
Simplifying:
y - 4 = -1/6(x + 6)
Multiplying both sides by 6 to get rid of the fraction:
6y - 24 = -x - 6
Rearranging the terms:
x + 6y = -18
Dividing both sides by -1:
-x - 6y = 18
Thus, the correct equation for the line is y = -1/6x + 3.
Therefore, the answer is B.