Final answer:
The equation of a line perpendicular to f(x)=-2x+1 and passing through the point (-1,3) is y= (1/2)x + 3/2. Option d is correct.
Step-by-step explanation:
To find the equation of a line perpendicular to the given function f(x) = -2x + 1 through the point (-1, 3), we can use the fact that the slopes of perpendicular lines are negative reciprocals of each other.
The given function has a slope of -2.
Therefore, the slope of the line perpendicular to it will be the negative reciprocal of -2, which is 1/2.
We can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form is y - y_1 = m(x - x_1), where (x_1, y_1) is the given point and m is the slope.
Substituting the given point (-1, 3) and the slope 1/2 into the point-slope form gives us:
y - 3 = (1/2)(x + 1)
y = (1/2)x + 3/2
Therefore, the equation of a line perpendicular to f(x) = -2x + 1 through the point (-1, 3) is y = (1/2)x + 3/2.
Complete question:
Write the equation of a line perpendicular to f(x)=−2x+1 through the point (-1,3). a) y=2x+1 b) y=−2x−1 c) y=−2x+3 d) y=(1/2)x + 3/2.