Answer:
A line that is perpendicular to the line y=-2x+1 will have a slope that is the negative reciprocal of -2, which is 1/2.
The equation of a line in point-slope form is:
y - y1 = m(x - x1)
Where m is the slope of the line, and (x1, y1) is a point on the line.
Given that the point (-4,3) lies on the line, we can substitute those values for x1 and y1:
y - 3 = 1/2(x + 4)
Which is the equation of a line that is perpendicular to y=-2x+1 that passes through the point (-4,3).
Alternatively, you can also write the equation of a line in slope-intercept form y = mx + b,
The slope of a line perpendicular to y=-2x+1 is 1/2, therefore m = 1/2
We can substitute the point (-4,3) in the equation y = mx + b,
3 = (1/2)(-4) + b
b = 3.5
Therefore the equation of the line is y = 1/2x + 3.5