Question
what is the equation of a line perpendicular to y=3x-2 that passes through (2,-1)
A. y-1=-3(x+2)
B. y-1=-1/3(x+2)
C. y+1=-3(x-2)
D. y+1= -1/3(x-2)
A. y-1=-3(x+2)
B. y-1=-1/3(x+2)
C. y+1=-3(x-2)
D. y+1= -1/3(x-2)
Answers
GPT 3.5
To find the equation of a line perpendicular to y=3x-2, we need to find the negative reciprocal of the slope of the given line. The slope of y=3x-2 is 3, so the negative reciprocal is -1/3.
We are also given that the line passes through the point (2,-1). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - (-1) = -1/3(x - 2)
Simplifying the equation:
y + 1 = -1/3(x - 2)
This equation matches option D. Therefore, the equation of a line perpendicular to y=3x-2 that passes through (2,-1) is y+1= -1/3(x-2).
We are also given that the line passes through the point (2,-1). We can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Where (x1, y1) is the given point and m is the slope.
Plugging in the values, we have:
y - (-1) = -1/3(x - 2)
Simplifying the equation:
y + 1 = -1/3(x - 2)
This equation matches option D. Therefore, the equation of a line perpendicular to y=3x-2 that passes through (2,-1) is y+1= -1/3(x-2).