Which equation is the equation of a line that passes through (−6, 4)
and is perpendicular to y=6x−2
?(1 point)
Responses
y=−6x−32
y is equal to negative 6 x minus 32
y=−1/6x+3
y is equal to negative 1 sixth x plus 3
y=1/6x+5
y is equal to 1 sixth x plus 5
y=6x+40
Since we want to find a line that is perpendicular to y=6x-2, we need to find the negative reciprocal of the slope. The slope of y=6x-2 is 6. The negative reciprocal of 6 is -1/6.
Now, we can use the point-slope form of a linear equation to find the equation of the line passing through (-6, 4) with a slope of -1/6.
y - y1 = m(x - x1)
Plugging in the values (-6, 4) and -1/6 for x1, y1, and m, we get:
y - 4 = (-1/6)(x - (-6))
Simplifying this equation gives:
y - 4 = (-1/6)(x + 6)
Distributing -1/6 to (x + 6), we get:
y - 4 = -1/6x - 1
Adding 4 to both sides of the equation gives:
y = -1/6x - 1 + 4
Simplifying further gives:
y = -1/6x + 3
So, the equation of the line that passes through (-6, 4) and is perpendicular to y=6x-2 is y = -1/6x + 3.
Therefore, the correct answer is:
y=−1/6x+3